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Simplify n squared r to the fifth n to

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the negative seventh.

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Express your answer in exponential form

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with positive exponents.

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Let me just rewrite what they have up there.

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So we have n squared r to the fifth n to

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the negative seventh.

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So the easiest way to simplify this, I would say kind of just

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while we were multiplying them, group the common bases.

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So we have two exponent expressions with n as a base.

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We have n squared and we have n to the negative seventh.

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So let me just rearrange this multiplication right here.

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I can rewrite this as n squared n to the negative

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seven and then we have our r to the fifth.

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And what's this going to be equal to?

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Well we have n squared times n to the negative seven.

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We can add those two exponents.

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So this right here would simplify to n

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to the 2 minus 7.

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2 minus 7 is negative 5.

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N to the negative 5, r to the fifth.

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Now we've simplified this about as much as we can.

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But, we're not done yet.

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Because they said express your answer in exponential form

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with positive exponents.

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This is a negative exponent here.

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This is not acceptable, at least based on what

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they asked us to do.

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So we know that n to the negative fifth is the same

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thing as 1 over n to the fifth.

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So we can just rewrite it the that way.

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So this is the same thing as 1 over n to the fifth

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times r to the fifth.

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Or we could say this is equal to r to the fifth

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over n to the fifth.

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And this is about as simple as you can you can get.

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If you wanted to do other things here you could say that

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this is equal to r over n to the fifth.

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Since both of these are being raised to the fifth power.

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But this is probably what they want here.

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We've simplified it and all of the exponents are now positive

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because we put the n in the denominator.

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