How is 9^3/2 = 27?? i need the answer?

9^(3/2)

The rational exponent (3/2) contains these instructions

the denominator is asking for the root of the base

the numerator is saying 'raise to this power'

The square root (^1/2) of 9 is 3

The cube of 3 is 27

QED

9^(3/2) = 3^3 = 27

First do 9^1/2.
thats three right? Then do 3^3.
is 27! just do each seperately.

a^(m/n) ≡ ⁿ√(a^m) (n ≠ 0)

9^(3/2)
= √(9^3)
= √[(3^2)^3]
= √[(3^3)^2]
= 3^3
= 27

You can do this in two (2) steps:

Step 1 -- extract the square root of 9

9^1/2 = 3


Step 2 -- take the cube of the answer in Step 1

3^3 = 3 * 3 * 3 = 27

Hope this helps.

It's because it's 9^(3/2). When powers are expressed in fractions, that means that the denominator of the fraction is the root, and the numerator is what the base is actually raised to.

9^(3/2) becomes √9^(3). (The square root of 9 raised to the third power.)
√9^(3)
√729
27

Try putting it into your calculator. =] Make sure you put parenthesis around the 3 if you're using the caret.

9^(3 / 2) * 9^(3 / 2)
= 9^3
= 729

[9^(3 / 2) ]^2 = 729
9^(3 / 2) = sqrt(729)
9^(3 / 2) = 27