Video: Simplifying Algebraic Expressions with Negative Exponents Using Laws of Exponents

Simplify π‘₯⁷ Γ— π‘₯⁻⁡ Γ— π‘₯⁴, where π‘₯ β‰  0.

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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‘Ž times π‘₯ to the 𝑏 is equal to π‘₯ to the π‘Ž plus 𝑏. So when we multiply things with like bases, we add their exponents. So we need to take this, keep our like base cause they’ll 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 let’s give it a try. So in the original problem, we have π‘₯ to the negative fifth power. When you have a negative exponent and it’s 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.

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