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.
