In Exercises 107–114, simplify each exponential expression. Assum...

Question

In Exercises 107–114, simplify each exponential expression. Assume that variables represent nonzero real numbers. (x^−2 y)^−3/(x^2 y^−1)^3

Accepted Answer

Hi everyone here's the next question. Consider the given exponential expression and simplify. So now I've got something in the numerator and something in the denominator in both cases something in parentheses raised to a power. So I'm gonna go ahead and rewrite it and I'm going to distribute that exponent outside the parentheses as my first step. So my numerator here in the parentheses I have eight to the -3. Be all raised to the negative five power. So let's rewrite that as eight. And when we raise something with an exponent to a power we multiply the exponents. So I have eight to them minus three times minus negatives equal positive. So I've got eight to the 15th power there and then my B. Doesn't have an exponents. So it's just B to the negative five power. That's my new marine. Er And then my denominator just help me keep it straight. I'm gonna write here in red, I have eight to the three power. B to the -1. All that in parentheses raised the fifth power. So then I have a to the third power times five. So that would be a to the 15th power. And then my B which is the negative one is B to the negative one times five. So that's B to the negative five in my denominator. Well let's look at this, I have the same terms in the numerator and denominator 1/15 B to the minus 5/8 of the 15th, even minus five. They all cancel out. And so that fraction equals one. It's the same on the numerator and denominator, So there's my answer choice, A one. See you in the next video.

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