what is the simplified value of the exponential expression $27^{\frac{1}{3}}$?\n$\frac{1}{3}$\n$\frac{1}{9}$\…

Explanation:

Step1: Rewrite 27 as a power of 3

We know that $27 = 3^3$. So, $27^{\frac{1}{3}}=(3^3)^{\frac{1}{3}}$.

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

According to the power - of - a - power rule $(a^m)^n=a^{mn}$. Here, $a = 3$, $m = 3$ and $n=\frac{1}{3}$. Then $(3^3)^{\frac{1}{3}}=3^{3\times\frac{1}{3}}$.

Step3: Calculate the exponent

$3\times\frac{1}{3}=1$, so $3^{3\times\frac{1}{3}} = 3^1=3$.

Answer:

C. 3