Video Transcript
Simplify π₯ to the seventh times π₯ to the negative fifth times π₯ to the fourth, where π₯ is not equal to zero.
We can use the rule where π₯ to the π times π₯ to the π is equal to π₯ to the π plus π. So when we multiply things with like bases, we add their exponents. So we need to take this, keep our like base cause theyβll have a base of π₯, and then add our exponents: seven plus negative five plus four, which gives us π₯ to the sixth.
And we get π₯ to the sixth. Now there is another way to do this. It may take a little bit longer, but letβs give it a try. So in the original problem, we have π₯ to the negative fifth power. When you have a negative exponent and itβs on a numerator, we move it to the denominator and make it positive.
Or vice versa, if it was a negative exponent on the denominator, we can move it up to the numerator. So what we can do, keep π₯ to the seventh and π₯ to the fourth on the numerator but move the π₯ to the negative fifth. So just like we did before, we need to add the seven and four together.
And seven plus four, and we get π₯ to the 11th. Now when we divide, we need to subtract our exponents. And 11 minus 5 gives us π₯ to the sixth. So once again π₯ to the sixth is our final answer.
