Question

please help 100 points wrong answers and links will be reported
Circle and Show!
(4 points each: 1 for the correct answer and 3 for supporting work!)
For numbers 8 -12, check the box next to the correct answer and type your work for that
problem.
Work must support your answer selection for credit!

Answer 1

Please find attached herewith the solutions of your questions.

Hope it helps.

If you have any query, feel free to ask.

Answer 2

Answer:

$\textsf{8.} \quad \textsf{B.}\;8x^3y$

$\textsf{9.} \quad \textsf{D.}\;81x^8$

$\textsf{10.} \quad \textsf{A.}\;10t^{-7}$

$\textsf{11.} \quad \textsf{C.}\;\dfrac{3m^2}{x^3}$

$\textsf{12.} \quad \textsf{B.}\;\dfrac{1}{3m^9}$

Step-by-step explanation:

Exponent Rules

$\textsf{Product rule}: \quad a^b \cdot a^c=a^{b+c}$

$\textsf{Power rule}: \quad (a^b)^c=a^{bc}$

$\textsf{Quotient rule} \quad \dfrac{a^b}{a^c}=a^{b-c}$

$\textsf{Power of a Product rule}: \quad (ab)^c=a^{c} \cdot b^c$

$\textsf{Negative exponent rule} \quad a^{-n}=\dfrac{1}{a^n}$

Question 8

$\begin{aligned}\left(2x^2y^3\right)\left(4xy^{-2}\right)&=2 \cdot 4 \cdot x^2 \cdot x \cdot y^3 \cdot y^{-2}\\&=8\cdot x^{(2+1)}\cdot y^{(3-2)}\\&=8 \cdot x^3 \cdot y^1\\&=8x^3y\end{aligned}$

Question 9

$\begin{aligned}\left(3x^2\right)^4&=3^4 \cdot (x^2)^4\\&=81 \cdot x^{(2 \cdot 4)}\\&=81x^8\end{aligned}$

Question 10

$\begin{aligned}5t^{-2} \cdot 2t^{-5}&=5 \cdot 2 \cdot t^{-2} \cdot t^{-5}\\&=10 \cdot t^{(-2-5)}\\&=10t^{-7}\end{aligned}$

Question 11

$\begin{aligned}\dfrac{6m^{10}x^4}{2m^8x^7}&=\dfrac{6}{2} \cdot \dfrac{m^{10}}{m^8} \cdot \dfrac{x^4}{x^7}\\\\&=3 \cdot m^{(10-8)} \cdot x^{(4-7)}\\\\&=3m^2x^{-3}\\\\&=\dfrac{3m^2}{x^3}\end{aligned}$

Question 12

$\begin{aligned}\dfrac{m^{-3}}{3m^6}&=\dfrac{1}{3} \cdot \dfrac{m^{-3}}{m^{6}}\\\\&=\dfrac{1}{3} \cdot m^{(-3-6)}\\\\&=\dfrac{1}{3} \cdot m^{-9}\\\\&=\dfrac{1}{3m^9}\end{aligned}$