In Exercises 73–84, simplify each expression using the quotients-...

Question

In Exercises 73–84, simplify each expression using the quotients-to-powers rule.

(- 3x/y)⁴

Accepted Answer

Hey, everyone in this problem, we're asked to simplify the following expression and write the answer with positive exponents. The expression given is -2 M divided by N all to the exponent six. We're given four answer choices. Option A 64 M to the exponent six N to the exponent six. Option B negative 64 N to the exponent six divided by M to the exponent six. Option C 64 M to the exponent six minus N to the exponent six. And option D 64 M to the exponent six divided by N to the exponent six. We're gonna start by rewriting the expression we were given. So we have negative two M divided by N all to the exponent six. Now when we have a fraction like this raised to an exponent, that exponent applies to the numerator and the denominator. So we can split this up and write it as -2 M to the exponent six divided by N to the exponent six. So we have the exponent applied to the numerator. The exponent applied to the denominator working with the numerator. We have negative two M to the exponent six, -2 to the exponent six is going to give us a value of 64. Can we have a negative value raised to an even power? So that's gonna be a positive. And then we have to the exponent six. And in the denominator, we have N to the exponent six into the exponent six. And this is our simplified expression. The exponents are all positive and that's what we were looking for. So the correct answer is 64 M to the exponent six divided by N to the exponent six, which corresponds with answer choice D. Thanks everyone for watching. I hope this video helped see you in the next one.

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In Exercises 73–84, simplify each expression using the quotients-to-powers rule. (- 3x/y)⁴