Question

create a question that requires all three exponent laws (multiplying and dividing powers with the same base,power of a power) are used to find the final answer. make the final answer

Answer 1

`\begin{gathered} \text{Multiplying powers with the same base:} \\ a^m\cdot a^n=a^(m+n) \\ \\ \text{Dividing powers with the same base:} \\ (a^m)/(a^n)=a^(m-n) \\ \\ \text{Power of power:} \\ (a^m)^n=a^(m\cdot n) \end{gathered}`

To get the given final answer using the three rules above you can create the next expression:

`-(3y^3)/(5y^2x^2x(z^2)^2)`

To solve it:

Use dividing powers with the same base to simplify the base y:

`-(3y^(3-2))/(5x^2x(z^2)^2)=-\frac{3y^{}}{5^{}x^2x(z^2)^2}`

Use multipliying powers with the same base to simplify the base x.

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

Use power of a power to simplify z:

`-\frac{3y^{}}{5x^3(z^(2\cdot2))}=-\frac{3y^{}}{5x^3z^4}`