Simplify the expression

(a^-5/4*c^1/4)^3

1 answer

To simplify the expression (a^(-5/4) * c^(1/4))^3, we can apply the power of a product rule, which states that (ab)^n = a^n * b^n. Using this rule, we can simplify the expression as follows:

(a^(-5/4))^3 * (c^(1/4))^3
= a^(-15/4) * c^(3/4)

To further simplify this expression, we can use the power of a power rule, which states that (a^n)^m = a^(n*m). Applying this rule, we get:

a^(-15/4) * c^(3/4)
= (a^(-15/4) * c^0) * c^(3/4)
= a^(-15) * c^(3/4)

Therefore, the simplified expression is a^(-15) * c^(3/4).