ShmoopTube

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And here's your shmoop du jour.

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Simplify 5a to the 8th times the square root of b to the 10th...

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times 2 times the square root of a to the 8th times b to the 10th.

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Here are the potential answers...

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Before we spoil the ending, hit pause and try to solve this baby yourself.

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The trickiest part of this expression is recognizing that when we square root a variable with an exponent...

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...the square root has the effect of dividing the exponent in half.

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So the square root of b to the 10th becomes b to the 5th, and the square root of a to

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the 8th becomes a to the 4th. The product of the coefficients 5 and 2 is

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just 5 times 2, or 10.

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The second important thing we need to know is that when we multiply monomials with the

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same base, we can just add the exponents.

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If we group like terms together, the product of the problem is 10 times a to the 8th times

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a to the 4th... times b to the 5th times b to the 10th.

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8 plus 4 equals 12, and 5 plus 10 equals 15...

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...so we have 10 times a to the 12th power time b to the 15th....

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...which gives us C.

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The greatest thing about performing this mathematical trick is that...

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...you can try this one at home.

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