simplify.\n81^{\frac{3}{4}}

Explanation:

Step1: Rewrite 81 as a power - base.

$81 = 3^4$, so $81^{\frac{3}{4}}=(3^4)^{\frac{3}{4}}$

Step2: Apply the power - of - a - power rule.

According to the rule $(a^m)^n=a^{mn}$, we have $(3^4)^{\frac{3}{4}} = 3^{4\times\frac{3}{4}}$

Step3: Calculate the exponent.

$4\times\frac{3}{4}=3$, so $3^{4\times\frac{3}{4}}=3^3$

Step4: Evaluate $3^3$.

$3^3 = 3\times3\times3=27$

Answer:

27