Simplify the expression a2c1535 Write your answer without us

Simplify the expression.

(a^2*c^-1/5)^3/5

Write your answer without using negative exponents.
Assume that all variables are positive real numbers.

Solution

We know that (p^x)^y = p^xy . Let 2c^-1/5 = x. Then (a^x)^3/5 = a^3x/5 . Now, 3x/5 = 3(2c^-1/5)/5 = (6/5)c^-1/5. Therefore

(a^ 2c^-1/5)^3/5 = (a)^(6/5)^c^-1/5. = 1/ (a)^{6/5c^1/5}