Exponent Problem >.<?

Question

If something has an exponent of a fraction, like 27^3/2, how would you go about simplifying it?

thanks!!

Answer 1

Raise the number to the power of the number in the top of the exponent, then take the bottom as the root

Example 4^(3/2)

= (4^3)^(1/2)

= 64^(1/2)

=8

[REPOST] When you post a problem with a fractional exponent, place the fraction in parentheses since order of operations is exponents before division, as in 27^(3/2). The way you have it, 27^3/2, is actually 1/2 times 27 cubed. It was clear what you really meant this time, not necessarily so next.

BW,
GH

Answer 2

27^(2/3) would be cube root of 27, which is 3, squared, so 9.

27^(3/2) is √(27^3) = √[(3•3•3)(3•3•3)(3•3•3)] that's 9 3's, and each pair is a 9 which has a square root of 3, so 3^4 times √3, that's 81√3.

Or you could say that since 27 = 3^3, 27^(3/2) = (3^3)^(3/2) = 3^(9/2) = (3^4)(3^1/2) = 81√3.

Thing about exponents is there's more than 1 way to think about it. Usually, find the root first, then the power, since that keeps the numbers you're thinking about smaller.

Answer 3

27^(3/2) = (27x27x27)^(1/2) = sqr(19683) = 140.296