Question

simplify.
27^{-\frac{1}{3}}

Explanation:

Step1: Rewrite 27 as a power of 3

$27 = 3^3$
So, $27^{-\frac{1}{3}}=(3^3)^{-\frac{1}{3}}$

Step2: Apply power - of - a - power rule

$(a^m)^n=a^{mn}$. Here $a = 3$, $m = 3$, $n=-\frac{1}{3}$
$(3^3)^{-\frac{1}{3}}=3^{3\times(-\frac{1}{3})}$

Step3: Calculate the exponent

$3\times(-\frac{1}{3})=- 1$
So, $3^{3\times(-\frac{1}{3})}=3^{-1}$

Step4: Use negative - exponent rule

$a^{-n}=\frac{1}{a^n}$. Here $a = 3$ and $n = 1$
$3^{-1}=\frac{1}{3}$

Answer:

$\frac{1}{3}$