Simplify the expressions using the quotient to a power property. ( p q ) 7 \left(\frac{p}{q}\right)^7

Everybody. So let's get started with our practice set. Hopefully, you get a chance to work these out and try these on your own before just guessing the answers. Let's get started here. We're gonna simplify this following expression using the quotient to a power property. This is also sometimes known as the power of a quotient rule. We've got p divided by q all raised to the seventh power. Now, if you remember from our video, just like the power of a product rule, whenever we see terms inside of fractions or expressions like this with an exponent outside, we distribute the exponent. In the case of a quotient, we distribute the exponent to both the numerator and also to the denominator and then we simplify afterwards. Alright? So if we do this, we're going to basically distribute this seven exponents to the p to get p to the seventh power divided by and then seven to the q on the denominator to get q to the seventh. And that's really all we do here. So remember, as a reminder, if we're gonna simplify the expressions, you may have to do some simplifying after the fact. Typically, when we have variables raised to exponents, you can't really do anything anymore. But if you have numbers raised to exponents, like for example two to the third power, you can turn that into a number like eight. And so that's part of the simplification process. We can't really do that here because all we have is just p to the seventh over q to the seventh. You can't really make that any simpler. And so that's the answer. Let's get started a couple more and hopefully you get a chance to try these out.