Combine and simplify the following radical expression 1/3^3radical81

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12-04-2018
Mathematics

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Combine and simplify the following radical expression 1/3^3radical81

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BabiiMuffin BabiiMuffin · Answer 1 · 2018-04-17T10:43:59+02:00

BabiiMuffin BabiiMuffin

17-04-2018

1/3^3 = 1/(3*3*3)
3*3 = 9
3*3*3 = 27
so 1/3^3 = 27

radical 81 = sqrt 81
81 = 9*9
9 = 3*3
so 81 = 3*3*3*3 = 3^4

sqrt 81 = sqrt (3^4)
sqrt of a number has its exponents as ^n/2, where n = 4 in this case
sqrt 81 = 3^2 = 9

1/3^3radical81 = 1/(3^3) * sqrt(3^4) = 1/27 * 9 = 9/27 = 1/3

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