Question

Use the product rule to simplify (xy^7)^10. What is the simplified expression?

Answer 1

Hello there. To solve this question, we'll have to remember some properties about exponentiation.

We have the following expression:

`(xy^7)^(10)`

First, remember the power product rule:

`(ab)^n=a^nb^n`

And the power of a power rule:

`(a^n_{})^m=a^(n\cdot m)`

In this case, we have:

Applying the power product rule

`(xy^{7^{}})^(10)=x^{10^{}^{}}(y^7)^(10)`

Now, apply the power of a power rule

`x^(10)(y^7_{})^(10)=x^(10)y^(7\cdot10)=x^(10)y^(70)`

This is the simplified form of this expression.