ShmoopTube

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And here's your shmoop du jour.

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Simplify the expression (4a to the -2) quantity to the -1.

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And here are the possible answers...

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Ok, this question is testing whether we have learned to love the negative exponent.

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And yeah, negative exponents just mean "one over", more or less.

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Remember order of operations, or PEMDAS?

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This tells us that we have to start with the parentheses to simplify this expression.

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So let's start in the middle of the cave and clean up the mess in... 4a to the -2.

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Think about this one as 4 times... big pause...

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"a" to the -2.

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That is, first get "a" to the -2 to be 1 over "a" squared.

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That'll help simplify things a lot. And we then have 4 times that number...

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which gives us 4 over "a" squared. Now that we've manipulated the inside of the

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parentheses, we can work on the exponent.

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So think of 4 over "a" squared as one unit for now, one thing that can't be changed...

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for a moment anyway.

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That whole chunk of number is now placed to the -1...

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...which means that we take one OVER that number to then get rid of the negative exponent

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thingy... which is just too odd to digest. So we have 1 OVER the quantity 4 over "a" squared.

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Remember that dividing by a fraction is the same as multiplying the inverse -- so let's do that.

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We get one TIMES "a" squared over 4. Which is just "a" squared over 4.

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And ta-da.. the answer is B.

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