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{ }(.)/(.)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: }(x^a)/(x^b)=x^(a-b) \end{gathered}`

Step 3:

Simplify

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