Simplify each of the following problems. Write all answers with positive exponents and simplified radical form.

Question

1:
(64m^2)^3/2

2:
(m x m^-2 n^1/3)^2

3:
a^5/6 b^2/6

4:
4x^-2/-4
___
8x^1/3

Answer 1

(64m^2)^3/2 = 64^3/2 * (m^2)^3/2 = 512m^3
(m x m^-2 n^1/3)^2 = (m^-1 n^1/3)^2 = m^-2 n^2/3
a^5/6 b^2/6 = (a^5 b^2)^1/6

(4x^-2)/-4
------------ = (-x^-2)/(8x^1/3) = -1/(8 x^(7/3) )
8x^1/3