What is the easiest way to solve a fractions that has an exponents

how does 4^5/2 becomes 32?

I'm confused because i thought x^(a/b) can be written as (^b√x)^a

ok in a problem like this you do this:

because the number in the denominator is a 2 we simplify to say (square root of 4)^5. Therfore the sqr root of 4 is 2 and 2^5 is 32. If the number in the denominator was a 3 we would say
(cube root of 4)^5.

Hope this helps!

how does 4^5/2 becomes 32?

The exponent is the number of times that the number is used as a factor
5/2 = 2 ½
So 4 is used 2 ½ times
½ of 4 = 2
4^ 2 ½ = 4 * 4 * 2 = 32

OR

4 = 2 * 2
(2 * 2)^5/2 = 2 * 2 * 2 * 2 * 2 = 2^5 = 32

4^5/2=512
because 4^5 means 4 x 4 x 4 x 4 x 4= 1024 then divide so, 1024/2 = 512 (:
So, the answer is 512 (:

4^(5/2) = (4^½)⁵ = (2)⁵ = 32

4^5/2

= (2^2)^(5/2) /// 4 = 2x2 = 2^2

= 2^( 2*5/2)

= 2^5

= 2x 2x2x2x2

= 32

4^(5/2)

=√(4^5)

=√1024

=32