In Exercises 35–52, write each expression with positive exponents...

Question

In Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible.

x⁻²/y⁻⁵

Accepted Answer

Hey, everyone in this problem, we're asked to simplify the following expression and to write the final answer using positive exponents. The expression given is M to the exponent - divided by N to the exponent -6. We're given four answer choices. Option A N to the exponent six multiplied by M to the exponent three. Option B N to the exponent six divided by M to the exponent three. Option C N to the exponent three divided by M to the exponent six. And option D N to the exponent three multiplied by M to the exponent six. We're gonna start by rewriting what we were given. So we have to exponent negative three, divided by N to the exponent -6. And we can rewrite this just to make it clear what we have here. This is equivalent to M to the exponent negative three multiplied by one divided by N to the exponent negative six. OK. These two are equivalent. So now we need two separate things to deal with. We have this F to the exponent negative three and we have this one divided by N to the exponent -6. Now recall the rule for dealing with negative exponents. If we have X to the exponent negative A, we can write this as a positive exponent by moving everything to the denominator. So X to the exponent negative A is equal to one divided by X to the exponent positive A. Now if A is negative, then this becomes X to the exponent B is equal to one divided by X to the exponent negative B. OK. These are the same expression we've just switched where the negative side is OK. So dealing with M to the exponent negative three, this looks like the first case, we have something to the exponent that's negative. In the numerator, we can write this as one divided by M Q. Then we're gonna multiply we have one divided by N to the exponent -6. It looks like the second case we had when we wrote down our rules. So we have a negative exponent in the denominator. We can write this as N to the exponent six. OK. We move it to the numerator that exponent becomes positive. So now we have one divided by M cubed multiplied by N to the exponent six. And we can simplify this as N to the exponent six divided by M cubed. This is our simplified expression. We have positive exponents. Now like we were asked, we get N to the exponent six divided by M cubed which corresponds with answer choice B. Thanks everyone for watching. I hope this video helped see you in the next one.

In Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. x⁻²/y⁻⁵

Key Concepts

Negative Exponents

Reciprocal

Simplification of Expressions

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