Question

Simplify the expression below and explain which rules of exponents you used to simplify the expression. (xy^7)^3 \div y^{14}

Answer 1

Step 1:

Write the expression

$(xy^7)^{3^{}}\text{ }\frac{.}{.}y^7$

Step 2:

Apply laws of exponent below to simplify the expression.

$\begin{gathered} \text{Power Law: (x}^a)^b=x^{ab} \\ \\ \text{Division law: }\frac{x^a}{x^b}=x^{a-b} \end{gathered}$

Step 3:

Simplify

$\begin{gathered} (xy^7)^3\text{ }\frac{.}{.}y^{14} \\ =\frac{(xy^7)^3}{y^{14}} \\ \text{Apply the power law to the numerator} \\ =\text{ }\frac{x^3y^{7\times3}}{y^{14}} \\ =\text{ }\frac{x^3y^{21}}{y^{14}} \\ Next,\text{ apply the division law} \\ =x^3y^{21-14} \\ =x^3y^7 \end{gathered}$