Unit 6 Test

Akwankyerɛ

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Perfect Squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

Perfect Cubes: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000

Perfect Fourths: 1, 16, 81, 256, 625, 1296, 2401, 4096, 6561, 10000

1

Which of the following is the simplified form of \sqrt[3]{81m^{8}n^{4}}?

3m^{2}n\sqrt[3]{3m^{2}n}

9m^{3}n\sqrt[3]{m^{2}n}

9m^{2}n\sqrt[3]{n}

3m^{2}n\sqrt[3]{3n}

1

Which of the following is the simplified form of 5xy\sqrt{28x}+\sqrt{63x^{3}y^{2}}?

13x^{2}y^{2}\sqrt{7x}

13xy\sqrt{7x}

29xy\sqrt{7x}

29x^{2}y^{2}\sqrt{7x}

1

Which of the following is the simplified form of 2\sqrt[4]{8w^{3}}\cdot 3\sqrt[4]{32w^{5}}?

24w^{2}

96w^{3}\sqrt[4]{w^{3}}

96w^{2}

24w^{3}\sqrt[4]{w^{3}}

1

Simplify the expression below.
\sqrt{18}(2+\sqrt{6})-2\sqrt{3}
Do not include spaces or parentheses in your answer. Your answer should be two terms joined by addition/subtraction. Order does not matter. Simplify any radicals.

1

Simplify the expression below.
(4\sqrt{3}-1)(\sqrt{3}-6)
Do not include spaces or parentheses in your answer. Your answer should be two terms joined by addition/subtraction. Order does not matter. Simplify any radicals.

1

Simplify the expression below.
(2\sqrt{10}-\sqrt{6})(2\sqrt{10}+\sqrt{6})
Do not include spaces or parentheses in your answer.

1

Which of the following is the simplified form of \frac{\sqrt{294k^{30}}}{\sqrt{3k^{5}}}?

7k^{3}\sqrt{2}

7k^{5}\sqrt{2}

7k^{12}\sqrt{2k}

7k^{2}\sqrt{2}

1

Which of the following is the simplified form of \frac{\sqrt[3]{3}}{2\sqrt[3]{-375}}?

10

-10

-\frac{1}{10}

\frac{1}{10}

1

Which is equivalent to \sqrt{16x^{7}y^{4}}?

8x^{\frac{7}{2}}y^{2}

4x^{\frac{2}{7}}y^{\frac{1}{2}}

8x^{\frac{2}{7}}y^{\frac{1}{2}}

4x^{\frac{7}{2}}y^{2}

1

Which is equivalent to a^{\frac{5}{4}}b^{\frac{13}{4}}?

\frac{1}{4}\sqrt{a^{5}b^{13}}

a^{2}b^{6}\sqrt[4]{ab}

ab^{3}\sqrt[4]{ab}

a^{4}b^{4}\sqrt{ab}

1

Which of the following is the simplified form of (2x)^{\frac{1}{3}}\cdot (2x)^{\frac{4}{3}}?

4x\sqrt[3]{4x^{2}}

4x\sqrt[3]{2x}

2x\sqrt[3]{4x^{2}}

2x\sqrt[3]{2x}

1

Simplify the expression.
\frac{9^{\frac{7}{4}}}{9^{\frac{9}{4}}}
Do not use spaces. Your answer should be a rational number, in fraction form.

1

Which of the following is the simplified form of (p^{\frac{3}{2}})^{\frac{7}{2}}?

p^{2}\sqrt{p}

p^{5}\sqrt[4]{p}

p^{10}\sqrt{p}

p^{5}

1

Simplify the expression below.
\frac{(-54)^{2}}{\sqrt[3]{(-54)^{5}}}
Do not put spaces in your answer. Write your answer in simplest radical form.

1

Solve the equation. Check for extraneous solutions. Enter the solution as a number, no spaces. If there are two solutions, list them in increasing order separated by a comma. If there are no solutions, type "no solution" without quote marks.
\sqrt{6x-5}+1=8

1

Solve the equation. Check for extraneous solutions. Enter the solution as a number, no spaces. If there are two solutions, list them in increasing order separated by a comma. If there are no solutions, type "no solution" without quote marks.
-5\sqrt[3]{2x+3}=-15

1

Solve the equation. Check for extraneous solutions. Enter the solution as a number, no spaces. If there are two solutions, list them in increasing order separated by a comma. If there are no solutions, type "no solution" without quote marks.
7-(3x-29)^{\frac{1}{4}}=5

1

Solve the equation. Check for extraneous solutions. Enter the solution as a number, no spaces. If there are two solutions, list them in increasing order separated by a comma. If there are no solutions, type "no solution" without quote marks.
(7-2x)^{\frac{1}{2}}=(1-5x)^{\frac{1}{2}}

1

Solve the equation. Check for extraneous solutions. Enter the solution as a number, no spaces. If there are two solutions, list them in increasing order separated by a comma. If there are no solutions, type "no solution" without quote marks.
x = \sqrt{13x-40}

1

Solve the equation. Check for extraneous solutions. Enter the solution as a number, no spaces. If there are two solutions, list them in increasing order separated by a comma. If there are no solutions, type "no solution" without quote marks.
\sqrt{6x+15}-4=x

1

If f(x) = -\frac{1}{4}x-2, what is f^{-1}(x), the inverse?
Enter your answer as an expression, no "=" or spaces.

1

If f(x) = 2x+14, what is f^{-1}(x), the inverse?
Enter your answer as an expression, no "=" or spaces.

1

If f(x) = \sqrt[3]{4x-12}, what is f^{-1}(x), the inverse?
Enter your answer as an expression, no "=" or spaces.

1

If f(x) = (x+5)^{2}-3, what is f^{-1}(x), the inverse?
Enter your answer as an expression, no "=" or spaces.

1

Are the following functions inverses of each other?
f(x) = \frac{1}{3}x-3
g(x)=6x+18

yes

no

1

Are the following functions inverses of each other?
f(x)=\sqrt[4]{2x-6}
g(x)=\frac{1}{2}x^{4}+3

yes

no

Unit 6 Test

Which of the following is the simplified form of \sqrt[3]{81m^{8}n^{4}}?

Which of the following is the simplified form of 5xy\sqrt{28x}+\sqrt{63x^{3}y^{2}}?

Which of the following is the simplified form of 2\sqrt[4]{8w^{3}}\cdot 3\sqrt[4]{32w^{5}}?

Simplify the expression below.\sqrt{18}(2+\sqrt{6})-2\sqrt{3}Do not include spaces or parentheses in your answer. Your answer should be two terms joined by addition/subtraction. Order does not matter. Simplify any radicals.

Simplify the expression below.(4\sqrt{3}-1)(\sqrt{3}-6)Do not include spaces or parentheses in your answer. Your answer should be two terms joined by addition/subtraction. Order does not matter. Simplify any radicals.

Simplify the expression below.(2\sqrt{10}-\sqrt{6})(2\sqrt{10}+\sqrt{6})Do not include spaces or parentheses in your answer.

Which of the following is the simplified form of \frac{\sqrt{294k^{30}}}{\sqrt{3k^{5}}}?

Which of the following is the simplified form of \frac{\sqrt[3]{3}}{2\sqrt[3]{-375}}?

Which is equivalent to \sqrt{16x^{7}y^{4}}?

Which is equivalent to a^{\frac{5}{4}}b^{\frac{13}{4}}?

Which of the following is the simplified form of (2x)^{\frac{1}{3}}\cdot (2x)^{\frac{4}{3}}?

Simplify the expression.\frac{9^{\frac{7}{4}}}{9^{\frac{9}{4}}}Do not use spaces. Your answer should be a rational number, in fraction form.

Which of the following is the simplified form of (p^{\frac{3}{2}})^{\frac{7}{2}}?

Simplify the expression below.\frac{(-54)^{2}}{\sqrt[3]{(-54)^{5}}}Do not put spaces in your answer. Write your answer in simplest radical form.

Solve the equation. Check for extraneous solutions. Enter the solution as a number, no spaces. If there are two solutions, list them in increasing order separated by a comma. If there are no solutions, type "no solution" without quote marks.\sqrt{6x-5}+1=8

Solve the equation. Check for extraneous solutions. Enter the solution as a number, no spaces. If there are two solutions, list them in increasing order separated by a comma. If there are no solutions, type "no solution" without quote marks.-5\sqrt[3]{2x+3}=-15

Solve the equation. Check for extraneous solutions. Enter the solution as a number, no spaces. If there are two solutions, list them in increasing order separated by a comma. If there are no solutions, type "no solution" without quote marks.7-(3x-29)^{\frac{1}{4}}=5

Solve the equation. Check for extraneous solutions. Enter the solution as a number, no spaces. If there are two solutions, list them in increasing order separated by a comma. If there are no solutions, type "no solution" without quote marks.(7-2x)^{\frac{1}{2}}=(1-5x)^{\frac{1}{2}}

Solve the equation. Check for extraneous solutions. Enter the solution as a number, no spaces. If there are two solutions, list them in increasing order separated by a comma. If there are no solutions, type "no solution" without quote marks.x = \sqrt{13x-40}

Solve the equation. Check for extraneous solutions. Enter the solution as a number, no spaces. If there are two solutions, list them in increasing order separated by a comma. If there are no solutions, type "no solution" without quote marks.\sqrt{6x+15}-4=x

If f(x) = -\frac{1}{4}x-2, what is f^{-1}(x), the inverse?Enter your answer as an expression, no "=" or spaces.

If f(x) = 2x+14, what is f^{-1}(x), the inverse?Enter your answer as an expression, no "=" or spaces.

If f(x) = \sqrt[3]{4x-12}, what is f^{-1}(x), the inverse?Enter your answer as an expression, no "=" or spaces.

If f(x) = (x+5)^{2}-3, what is f^{-1}(x), the inverse?Enter your answer as an expression, no "=" or spaces.

Are the following functions inverses of each other?f(x) = \frac{1}{3}x-3g(x)=6x+18

Are the following functions inverses of each other?f(x)=\sqrt[4]{2x-6}g(x)=\frac{1}{2}x^{4}+3

Which of the following is the simplified form of \sqrt[3]{81m^{8}n^{4}}?

Which of the following is the simplified form of 5xy\sqrt{28x}+\sqrt{63x^{3}y^{2}}?

Which of the following is the simplified form of 2\sqrt[4]{8w^{3}}\cdot 3\sqrt[4]{32w^{5}}?

Simplify the expression below.\sqrt{18}(2+\sqrt{6})-2\sqrt{3}Do not include spaces or parentheses in your answer. Your answer should be two terms joined by addition/subtraction. Order does not matter. Simplify any radicals.

Simplify the expression below.(4\sqrt{3}-1)(\sqrt{3}-6)Do not include spaces or parentheses in your answer. Your answer should be two terms joined by addition/subtraction. Order does not matter. Simplify any radicals.

Simplify the expression below.(2\sqrt{10}-\sqrt{6})(2\sqrt{10}+\sqrt{6})Do not include spaces or parentheses in your answer.

Which of the following is the simplified form of \frac{\sqrt{294k^{30}}}{\sqrt{3k^{5}}}?

Which of the following is the simplified form of \frac{\sqrt[3]{3}}{2\sqrt[3]{-375}}?

Which is equivalent to \sqrt{16x^{7}y^{4}}?

Which is equivalent to a^{\frac{5}{4}}b^{\frac{13}{4}}?

Which of the following is the simplified form of (2x)^{\frac{1}{3}}\cdot (2x)^{\frac{4}{3}}?

Simplify the expression.\frac{9^{\frac{7}{4}}}{9^{\frac{9}{4}}}Do not use spaces. Your answer should be a rational number, in fraction form.

Which of the following is the simplified form of (p^{\frac{3}{2}})^{\frac{7}{2}}?

Simplify the expression below.\frac{(-54)^{2}}{\sqrt[3]{(-54)^{5}}}Do not put spaces in your answer. Write your answer in simplest radical form.

Solve the equation. Check for extraneous solutions. Enter the solution as a number, no spaces. If there are two solutions, list them in increasing order separated by a comma. If there are no solutions, type "no solution" without quote marks.\sqrt{6x-5}+1=8

Solve the equation. Check for extraneous solutions. Enter the solution as a number, no spaces. If there are two solutions, list them in increasing order separated by a comma. If there are no solutions, type "no solution" without quote marks.-5\sqrt[3]{2x+3}=-15

Solve the equation. Check for extraneous solutions. Enter the solution as a number, no spaces. If there are two solutions, list them in increasing order separated by a comma. If there are no solutions, type "no solution" without quote marks.7-(3x-29)^{\frac{1}{4}}=5

Solve the equation. Check for extraneous solutions. Enter the solution as a number, no spaces. If there are two solutions, list them in increasing order separated by a comma. If there are no solutions, type "no solution" without quote marks.(7-2x)^{\frac{1}{2}}=(1-5x)^{\frac{1}{2}}

Solve the equation. Check for extraneous solutions. Enter the solution as a number, no spaces. If there are two solutions, list them in increasing order separated by a comma. If there are no solutions, type "no solution" without quote marks.x = \sqrt{13x-40}

Solve the equation. Check for extraneous solutions. Enter the solution as a number, no spaces. If there are two solutions, list them in increasing order separated by a comma. If there are no solutions, type "no solution" without quote marks.\sqrt{6x+15}-4=x

If f(x) = -\frac{1}{4}x-2, what is f^{-1}(x), the inverse?Enter your answer as an expression, no "=" or spaces.

If f(x) = 2x+14, what is f^{-1}(x), the inverse?Enter your answer as an expression, no "=" or spaces.

If f(x) = \sqrt[3]{4x-12}, what is f^{-1}(x), the inverse?Enter your answer as an expression, no "=" or spaces.

If f(x) = (x+5)^{2}-3, what is f^{-1}(x), the inverse?Enter your answer as an expression, no "=" or spaces.

Are the following functions inverses of each other?f(x) = \frac{1}{3}x-3g(x)=6x+18

Are the following functions inverses of each other?f(x)=\sqrt[4]{2x-6}g(x)=\frac{1}{2}x^{4}+3

Simplify the expression below.
\sqrt{18}(2+\sqrt{6})-2\sqrt{3}
Do not include spaces or parentheses in your answer. Your answer should be two terms joined by addition/subtraction. Order does not matter. Simplify any radicals.

Simplify the expression below.
(4\sqrt{3}-1)(\sqrt{3}-6)
Do not include spaces or parentheses in your answer. Your answer should be two terms joined by addition/subtraction. Order does not matter. Simplify any radicals.

Simplify the expression below.
(2\sqrt{10}-\sqrt{6})(2\sqrt{10}+\sqrt{6})
Do not include spaces or parentheses in your answer.

Simplify the expression.
\frac{9^{\frac{7}{4}}}{9^{\frac{9}{4}}}
Do not use spaces. Your answer should be a rational number, in fraction form.

Simplify the expression below.
\frac{(-54)^{2}}{\sqrt[3]{(-54)^{5}}}
Do not put spaces in your answer. Write your answer in simplest radical form.

Solve the equation. Check for extraneous solutions. Enter the solution as a number, no spaces. If there are two solutions, list them in increasing order separated by a comma. If there are no solutions, type "no solution" without quote marks.
\sqrt{6x-5}+1=8

Solve the equation. Check for extraneous solutions. Enter the solution as a number, no spaces. If there are two solutions, list them in increasing order separated by a comma. If there are no solutions, type "no solution" without quote marks.
-5\sqrt[3]{2x+3}=-15

Solve the equation. Check for extraneous solutions. Enter the solution as a number, no spaces. If there are two solutions, list them in increasing order separated by a comma. If there are no solutions, type "no solution" without quote marks.
7-(3x-29)^{\frac{1}{4}}=5

Solve the equation. Check for extraneous solutions. Enter the solution as a number, no spaces. If there are two solutions, list them in increasing order separated by a comma. If there are no solutions, type "no solution" without quote marks.
(7-2x)^{\frac{1}{2}}=(1-5x)^{\frac{1}{2}}

Solve the equation. Check for extraneous solutions. Enter the solution as a number, no spaces. If there are two solutions, list them in increasing order separated by a comma. If there are no solutions, type "no solution" without quote marks.
x = \sqrt{13x-40}

Solve the equation. Check for extraneous solutions. Enter the solution as a number, no spaces. If there are two solutions, list them in increasing order separated by a comma. If there are no solutions, type "no solution" without quote marks.
\sqrt{6x+15}-4=x

If f(x) = -\frac{1}{4}x-2, what is f^{-1}(x), the inverse?
Enter your answer as an expression, no "=" or spaces.

If f(x) = 2x+14, what is f^{-1}(x), the inverse?
Enter your answer as an expression, no "=" or spaces.

If f(x) = \sqrt[3]{4x-12}, what is f^{-1}(x), the inverse?
Enter your answer as an expression, no "=" or spaces.

If f(x) = (x+5)^{2}-3, what is f^{-1}(x), the inverse?
Enter your answer as an expression, no "=" or spaces.

Are the following functions inverses of each other?
f(x) = \frac{1}{3}x-3
g(x)=6x+18

Are the following functions inverses of each other?
f(x)=\sqrt[4]{2x-6}
g(x)=\frac{1}{2}x^{4}+3

Simplify the expression below.
\sqrt{18}(2+\sqrt{6})-2\sqrt{3}
Do not include spaces or parentheses in your answer. Your answer should be two terms joined by addition/subtraction. Order does not matter. Simplify any radicals.

Simplify the expression below.
(4\sqrt{3}-1)(\sqrt{3}-6)
Do not include spaces or parentheses in your answer. Your answer should be two terms joined by addition/subtraction. Order does not matter. Simplify any radicals.

Simplify the expression below.
(2\sqrt{10}-\sqrt{6})(2\sqrt{10}+\sqrt{6})
Do not include spaces or parentheses in your answer.

Simplify the expression.
\frac{9^{\frac{7}{4}}}{9^{\frac{9}{4}}}
Do not use spaces. Your answer should be a rational number, in fraction form.

Simplify the expression below.
\frac{(-54)^{2}}{\sqrt[3]{(-54)^{5}}}
Do not put spaces in your answer. Write your answer in simplest radical form.

Solve the equation. Check for extraneous solutions. Enter the solution as a number, no spaces. If there are two solutions, list them in increasing order separated by a comma. If there are no solutions, type "no solution" without quote marks.
\sqrt{6x-5}+1=8

Solve the equation. Check for extraneous solutions. Enter the solution as a number, no spaces. If there are two solutions, list them in increasing order separated by a comma. If there are no solutions, type "no solution" without quote marks.
-5\sqrt[3]{2x+3}=-15

Solve the equation. Check for extraneous solutions. Enter the solution as a number, no spaces. If there are two solutions, list them in increasing order separated by a comma. If there are no solutions, type "no solution" without quote marks.
7-(3x-29)^{\frac{1}{4}}=5

Solve the equation. Check for extraneous solutions. Enter the solution as a number, no spaces. If there are two solutions, list them in increasing order separated by a comma. If there are no solutions, type "no solution" without quote marks.
(7-2x)^{\frac{1}{2}}=(1-5x)^{\frac{1}{2}}

Solve the equation. Check for extraneous solutions. Enter the solution as a number, no spaces. If there are two solutions, list them in increasing order separated by a comma. If there are no solutions, type "no solution" without quote marks.
x = \sqrt{13x-40}

Solve the equation. Check for extraneous solutions. Enter the solution as a number, no spaces. If there are two solutions, list them in increasing order separated by a comma. If there are no solutions, type "no solution" without quote marks.
\sqrt{6x+15}-4=x

If f(x) = -\frac{1}{4}x-2, what is f^{-1}(x), the inverse?
Enter your answer as an expression, no "=" or spaces.

If f(x) = 2x+14, what is f^{-1}(x), the inverse?
Enter your answer as an expression, no "=" or spaces.

If f(x) = \sqrt[3]{4x-12}, what is f^{-1}(x), the inverse?
Enter your answer as an expression, no "=" or spaces.

If f(x) = (x+5)^{2}-3, what is f^{-1}(x), the inverse?
Enter your answer as an expression, no "=" or spaces.

Are the following functions inverses of each other?
f(x) = \frac{1}{3}x-3
g(x)=6x+18

Are the following functions inverses of each other?
f(x)=\sqrt[4]{2x-6}
g(x)=\frac{1}{2}x^{4}+3