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

`\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.}\;(3m^2)/(x^3)`

`\textsf{12.} \quad \textsf{B.}\;(1)/(3m^9)`

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

Question 12

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