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P6.2: Rational Exponents Conversion
By Katherine Rorabaugh
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Last updated about 4 years ago
12 questions
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Watch this video (and check out the practice problems) for more review with rational exponents.
Watch this video (and check out the practice problems) for more review with rational exponents.
Question 1
1.
Which property of exponents helps us define rational exponents?
product rule: a^{m} \cdot a^{n} = a^{m+n}
division rule: \frac{a^{m}}{a^{n}}=a^{m-n}
zero rule: a^{0} = 1
power rule: (a^{m})^{n} = a^{mn}
Question 2
2.
Rewrite the expression in exponential form.
Distribute the power
where possible.
\sqrt{3ab}
Your answer should have no spaces, and should have rational exponent(s).
Question 3
3.
Rewrite the expression in exponential form.
\sqrt[4]{18x^{6}y^{2}}
Your answer should be a term raised to a rational exponent.
Question 4
4.
Simplify. Give your answers in integer form, no spaces.
9^{\frac{1}{2}}\cdot9^{\frac{5}{2}}
Question 5
5.
Simplify. Give your answers in simplest radical form, no spaces.
\frac{x^{\frac{7}{3}}}{x^{\frac{2}{3}}}
Question 6
6.
Simplify. Give your answers in simplest radical form, no spaces.
(28^{\frac{3}{5}})^{\frac{5}{6}}
Question 7
7.
Simplify. Give your answers in simplest radical form, no spaces.
45^{-\frac{3}{2}}\cdot45^{2}
Question 8
8.
Simplify. Give your answers in simplest radical form, no spaces.
\sqrt[4]{p}\cdot\sqrt{p^{3}}
Question 9
9.
Simplify. Give your answers in simplest radical form, no spaces.
\frac{16}{\sqrt[4]{16^{3}}}
Question 10
10.
Simplify. Give your answers in simplest radical form, no spaces.
\sqrt[4]{16w^{6}}
Question 11
11.
REVIEW
Write the expression in simplest radical form.
\sqrt[3]{80a^{4}b^{6}}
Question 12
12.
REVIEW
Write the expression in simplest radical form.
\sqrt[4]{48x^{3}y^{8}z^{13}}