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

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

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

$-\frac{3y^3}{5y^2x^2x(z^2)^2}$

To solve it:

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

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

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:

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