Algebra LS-2 Quiz v1

Nota Bene
\color{red} \textrm{Show Your Work}! You must show your work with enough detail to clearly indicate:
Which exponent law/property you used
That you solved the problem algebraically (with equation-based methods)
Even with the correct answer, responses without enough work will receive no credit.

Finally, when possible, remember that it is best to write polynoials arranging each monomial term with variables in alphabetical order. And the monomials within a polynomials should be listed by descending degree.

Apply the "product rule" to the following expression as a (single) base raised to a (single) power.

a^{p}a^{-3p}a^{q}

Apply the "quotient rule" to the following expression to generate an equivalent expression.
\frac{h^{m}x^{-3}}{h^{n}x}

HINT: If you're having trouble, split the problem into two, easier problems by rewriting the expression as a product \frac{h^{m}x^{-3}}{h^{n}x}=\frac{h^{m}}{h^{n}}\cdot \frac{x^{-3}}{x}

Which of the following correctly defines the meaning of a negative exponent? Select all that apply.

Use the laws of exponents to write an equivalent expression that is maximally concise.

(4r^{0})^4

Use the laws of exponents to write an equivalent expression that is maximally concise.
4a^{3}b^{2}\cdot 3a^{-4}b^{-3}

Use the laws of exponents to write an equivalent expression that is maximally concise.
\frac{3x^{3}y^{-1}z^{-1}}{x^{-4}y^{0}z^{0}}

Use the laws of exponents to write an equivalent expression that is maximally concise.
\frac{2x^{2}y^{4}\cdot 4x^{2}y^{4} \cdot 3x}{3x^{-3}y^{2}}

Use the laws of exponents to write an equivalent expression that is maximally concise.
\frac{(2x^{3}z^{2})^{3}}{x^{3}y^{4}z^{2}\cdot x^{-4}z^{3}}

Multiply:

(x^{2}+\frac{1}{5}y)(y-3)

Multiply:

2h(h^{4}+j^{2}-9)

Every degree-3 polynomial in one variable can be expressed as ax^{3}+bx^{2}+cx^{1}+dx^{0} \textrm{, where } a, b, c, d \in \mathbb{R} \textrm{ and } a\neq0

Create an example where adding two, degree 3 polynomials does not yield another degree 3 polynomial.

Is the set of polynomials in one variable closed under addition? Explain your reasoning.

Note: Make sure you type enough here to make your thinking clear. Grading for this question will go by the quality of the explanation more than the accuracy of the answer.

Apply the "product rule" to the following expression as a (single) base raised to a (single) power.a^{p}a^{-3p}a^{q}

Which of the following correctly defines the meaning of a negative exponent? Select all that apply.

Use the laws of exponents to write an equivalent expression that is maximally concise.(4r^{0})^4

Use the laws of exponents to write an equivalent expression that is maximally concise.4a^{3}b^{2}\cdot 3a^{-4}b^{-3}

Use the laws of exponents to write an equivalent expression that is maximally concise.\frac{3x^{3}y^{-1}z^{-1}}{x^{-4}y^{0}z^{0}}

Use the laws of exponents to write an equivalent expression that is maximally concise.\frac{2x^{2}y^{4}\cdot 4x^{2}y^{4} \cdot 3x}{3x^{-3}y^{2}}

Use the laws of exponents to write an equivalent expression that is maximally concise.\frac{(2x^{3}z^{2})^{3}}{x^{3}y^{4}z^{2}\cdot x^{-4}z^{3}}

Multiply:(x^{2}+\frac{1}{5}y)(y-3)

Multiply:2h(h^{4}+j^{2}-9)

Every degree-3 polynomial in one variable can be expressed as ax^{3}+bx^{2}+cx^{1}+dx^{0} \textrm{, where } a, b, c, d \in \mathbb{R} \textrm{ and } a\neq0Create an example where adding two, degree 3 polynomials does not yield another degree 3 polynomial.

Is the set of polynomials in one variable closed under addition? Explain your reasoning.Note: Make sure you type enough here to make your thinking clear. Grading for this question will go by the quality of the explanation more than the accuracy of the answer.

Apply the "product rule" to the following expression as a (single) base raised to a (single) power.

a^{p}a^{-3p}a^{q}

Use the laws of exponents to write an equivalent expression that is maximally concise.

(4r^{0})^4

Use the laws of exponents to write an equivalent expression that is maximally concise.
4a^{3}b^{2}\cdot 3a^{-4}b^{-3}

Use the laws of exponents to write an equivalent expression that is maximally concise.
\frac{3x^{3}y^{-1}z^{-1}}{x^{-4}y^{0}z^{0}}

Use the laws of exponents to write an equivalent expression that is maximally concise.
\frac{2x^{2}y^{4}\cdot 4x^{2}y^{4} \cdot 3x}{3x^{-3}y^{2}}

Use the laws of exponents to write an equivalent expression that is maximally concise.
\frac{(2x^{3}z^{2})^{3}}{x^{3}y^{4}z^{2}\cdot x^{-4}z^{3}}

Multiply:

(x^{2}+\frac{1}{5}y)(y-3)

Multiply:

2h(h^{4}+j^{2}-9)

Every degree-3 polynomial in one variable can be expressed as ax^{3}+bx^{2}+cx^{1}+dx^{0} \textrm{, where } a, b, c, d \in \mathbb{R} \textrm{ and } a\neq0

Create an example where adding two, degree 3 polynomials does not yield another degree 3 polynomial.

Is the set of polynomials in one variable closed under addition? Explain your reasoning.

Note: Make sure you type enough here to make your thinking clear. Grading for this question will go by the quality of the explanation more than the accuracy of the answer.