Evaluate 27^(1/3)=3

$27^{\frac{1}{3}} = 3$

Step 1

Simplify the expression.

Rewrite $27$ as $3^{3}$ .

${(3^{3})}^{\frac{1}{3}} = 3$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$3^{3 (\frac{1}{3})} = 3$

Step 2

Cancel the common factor of $3$ .

Cancel the common factor.

$3^{3 (\frac{1}{3})} = 3$

Rewrite the expression.

$3^{1} = 3$

Step 3

Evaluate the exponent.

$3 = 3$