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. We're told to write the answer using positive exponents. The expression given is -8 to the exponent -2. We have four answer choices. Option A is one divided by eight squared or one divided by 64. Option B is negative one divided by eight squared or negative one divided by 64. Option C is negative eight squared or negative 64. And option D is one divided by eight squared or negative one divided by 64. Now we're gonna start by writing the expression we were given negative eight to the exponent -2. Now we want to deal with that negative exponent and recall if we have a negative exponent, say we have X to the exponent negative end, we can write this as one divided by X to the exponent X. So we put the base in the denominator and the exponent becomes positive, applying this to our problems. We have to be a little bit careful, we have this negative open front but the exponent -2 is not applied to that negative and there's no brackets that exponent does not apply to a negative sign. So we're gonna have negative and then we're gonna have whatever eight to the exponent negative two is OK. So if we apply negative exponent rule 8 to the exponent -2, it's going to be one over and one divided by eight squared. So we've moved our base to the denominator, the exponent becomes positive and now we can apply this negative sign out in front to our expression in brackets. And so we have negative one divided by eight squared. If we simplify in the denominator, eight squared is equal to 64. And so we get negative one divided by 64. This is the result we were looking for, this is a simplified expression where we have positive exponents. If we compare this to our answer traces, we found that the simplified expression is negative one divided by eight squared, which is equal to negative one divided by 64. 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

Simplifying Expressions

Exponent Rules

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