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.3⁻²

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 we're given is 4 to the exponent -2. We have four answer choices. Option A one divided by four squared or one divided by 16. Option B four squared or 16. Option C four squared or one divided by 16. And option D one divided by four squared or 16, we're gonna start by rewriting the expression we were given. So we have four to the exponent -2. And we're called the rule for dealing with negative exponents, we have X to the exponent negative N. We can write this as one divided by X to the exponent N. So if we put the base in the denominator, the exponent becomes positive applies to our problem. We have four to the exponent negative too. We wanna get this with a positive exponent. So we can write this as one divided by our base four and our exponent becomes positive one divided by four squared. We can simplify in the denominator four word is equal to 16. So we can write this as one divided by 16 as well. And that's our simplified expression with positive exponents. If we compare this with our answer choices, we found the answer to be one divided by four squared, which is equivalent to one divided by 16. This corresponds with answer choice. A 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.3⁻²

Key Concepts

Negative Exponents

Reciprocal

Simplification of Exponents

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