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.

(-5)⁻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 -9 all to the exponent -2. We have four answer choices. Option A -9 Squared or 1 divided by 81. Option B one divided by negative nine squared or one divided by 81. Option C -9 Squared or 81. And option D one divided by negative nine squared or negative one divided by 81. We're gonna start by rewriting the expression we were given. So we have negative nine brackets to the exponent -2. Now we're told we wanna write this using positive exponents so that negative exponent we have negative two. That's what we're gonna try to deal with first. So recall our rule for dealing with negative exponents. If we have X to the exponent negative N, we can write this as one divided by X to the exponent. And so we can move our base into the denominator and that exponent becomes positive. If we apply this to our problem, we have negative nine onto the exponent negative two. And it's important to note here that, that negative in negative nine is inside the bracket. That means that, that exponent is applied to that negative sign. OK. So when we apply our negative exponent rule, we need to consider the negative as part of the base. So again, -9 is a base. So you end up with one divided by negative nine and the exponent becomes positive. So we have neg um one divided by -9 to the exponent two. And we can simplify this negative nine squared. That's gonna give us positive 81. So we have one divided by 81. And that's the simplified expression we were looking for with positive exponents. If we compare those to our answer choices, we found that the answer is either one divided by negative nine all squared and this is equivalent to one divided by 81. This 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. (-5)⁻²

Key Concepts

Negative Exponents

Reciprocal

Simplification of Exponents

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