Question

Simplify the expression below. explain which exponent rules were used to simplify the expression.

Answer 1

Given the expression:

`\begin{gathered} \\ \\ \text{ (xy}^7)^3\text{ }/ y^(14) \end{gathered}`

Let's simplify the expression.

To simplify the expression, take the following steps.

Step 1:

Apply the product rule of exponents

`\begin{gathered} \text{ (xy}^7)^3\text{ }/ y^(14) \\ \\ =x^3\text{y}^7^((3))\text{ }/ y^(14) \\ \\ =\text{ }x^3\text{y}^(7\ast3)\text{ }/ y^(14) \\ \\ =\text{ }x^3\text{y}^(21)\text{ }/ y^(14) \end{gathered}`

Step 2:

Since we have the division sign here, we are to subtract to exponents that has the same bases.

Apply the division rule of exponents.

We have:

`\begin{gathered} \text{ }x^3y^(21)\text{ }/ y^(14) \\ \\ x^3y^(21-14) \\ \\ =x^3y^7 \end{gathered}`

ANSWER:

`x^3y^7`