ShmoopTube

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And here's your shmoop du jour.

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Simplify the expression n cubed squared times the square root of n to the 6th... all over n to the 8th.

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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 one yourself first.

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Remember order of operations or PEMDAS?

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Please Excuse My Dear Aunt Sally...

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or parentheses, exponents, multiplication/division, and addition/subtraction.

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PEMDAS tells us to work with the variables inside the parentheses first.

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n-cubed looks good... but the square root of n to the 6th gives us the effect of dividing

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its exponent value in half...

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...so the square root of n to the 6th can be simplified as n cubed.

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We can move to exponents next. Looking at our first quantity, we have the

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quantity n cubed... squared. One of the properties of exponents tells us

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that, for any number, a, with exponents m and n, a to the power of m,

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to the power of n, equals a to the power of m times n.

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This means that we multiply 3 and 2 in the

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expression n cubed squared, to get n to the 6th.

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Utilizing more properties of exponents... ...specifically, the one which states that

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a to the m times a to the n equals a to the m plus n... 

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and the one which states that a to the m over a to the n equals a to the m minus n...

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...we can add 6 plus 3 equals 9 to get n to the 9th in the numerator.

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The expression then becomes n to the 9th over n to the 8th.

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We can subtract 9 and 8 to get 1,

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so we're left with n to the first power, or just... n.

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Which is answer C.

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You'll need 'em again, so make sure you commit those properties of exponents to memory.

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Trust us... they're some of the most valuable properties on the board.

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