Algebra LS-2 Quiz v3

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.

w^{4}w^{-2r}

Apply the "quotient rule" to the following expression to generate an equivalent expression.
\frac{m^{-2}n^{10}}{m^{-7}n^{-3}}

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 is equivalent to y^4? Select all that apply.

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

\Big(\frac{p^{-6}q^{7}(p^{2}q)^{-3}}{(p^{-1}q^{-4})^{2}p^{10}}\Big)^{0}

Use the laws of exponents to write an equivalent expression that is maximally concise.
(-6x)^{2}

Use the laws of exponents to write an equivalent expression that is maximally concise.
\frac{a^{2}b^{-4}c^{-1}}{b^{-9}c^{8}a^{-4}}

Use the laws of exponents to write an equivalent expression that is maximally concise.
\frac{(6v^{2})^{-1}w^{-4}}{(2v)^{-3}w^{10}}

Decide whether the following equation is true or false. Explain your answer.

(-1)^{332}=1

N.B., the best possible explanation would be a proof (either that the statement is always true or that the statement is sometimes false).

Decide whether the following equation is true or false. Explain your answer.

(x+y)^{3}=x^{3}+y^{3}

N.B., the best possible explanation would be a proof (either that the statement is always true or that the statement is sometimes false).

Apply the "product rule" to the following expression as a (single) base raised to a (single) power.w^{4}w^{-2r}

Which of the following is equivalent to y^4? Select all that apply.

Use the laws of exponents to write an equivalent expression that is maximally concise.\Big(\frac{p^{-6}q^{7}(p^{2}q)^{-3}}{(p^{-1}q^{-4})^{2}p^{10}}\Big)^{0}

Use the laws of exponents to write an equivalent expression that is maximally concise.(-6x)^{2}

Use the laws of exponents to write an equivalent expression that is maximally concise.\frac{a^{2}b^{-4}c^{-1}}{b^{-9}c^{8}a^{-4}}

Use the laws of exponents to write an equivalent expression that is maximally concise.\frac{(6v^{2})^{-1}w^{-4}}{(2v)^{-3}w^{10}}

Decide whether the following equation is true or false. Explain your answer.(-1)^{332}=1N.B., the best possible explanation would be a proof (either that the statement is always true or that the statement is sometimes false).

Decide whether the following equation is true or false. Explain your answer.(x+y)^{3}=x^{3}+y^{3}N.B., the best possible explanation would be a proof (either that the statement is always true or that the statement is sometimes false).

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

w^{4}w^{-2r}

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

\Big(\frac{p^{-6}q^{7}(p^{2}q)^{-3}}{(p^{-1}q^{-4})^{2}p^{10}}\Big)^{0}

Use the laws of exponents to write an equivalent expression that is maximally concise.
(-6x)^{2}

Use the laws of exponents to write an equivalent expression that is maximally concise.
\frac{a^{2}b^{-4}c^{-1}}{b^{-9}c^{8}a^{-4}}

Use the laws of exponents to write an equivalent expression that is maximally concise.
\frac{(6v^{2})^{-1}w^{-4}}{(2v)^{-3}w^{10}}

Decide whether the following equation is true or false. Explain your answer.

(-1)^{332}=1

N.B., the best possible explanation would be a proof (either that the statement is always true or that the statement is sometimes false).

Decide whether the following equation is true or false. Explain your answer.

(x+y)^{3}=x^{3}+y^{3}

N.B., the best possible explanation would be a proof (either that the statement is always true or that the statement is sometimes false).