Question

Simplify. In the form of a paragraph, explain in complete sentences the steps necessary to simplify the expression andinclude the final answer in your explanation. Complete your work in the space provided or upload a file that can displaymath symbols if your work requires it.

Answer 1

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

1. When dividing with exponents, the exponent of a variable in the denominator is subtracted from the exponent in the numerator for the same variable. Then, first step to simplify is subtract the exponents of x and y in the fraction in parentheses:

$\begin{gathered} =(x^{3-1}y^{1-2})^{-2} \\ =(x^2y^{-1})^{-2} \end{gathered}$

2. To remove the parentheses you multiply each exponent in the parentheses by the exponent out of the parentheses:

$\begin{gathered} =x^{2\cdot(-2)}y^{(-1)\cdot(-2)} \\ \\ =x^{-4}y^2 \end{gathered}$

3. When you have a negative exponent (as the x powered to -4) you divide 1 in to the term with negative exponent (after you divide the exponent turns into a positive exponent):

$=\frac{1}{x^4}\cdot y^2$

4. Then, the given expression simplified is:

$(\frac{x^3y}{xy^2})^{-2}=\frac{y^2}{x^4}$