Evaluate (27^(5/3))^(1/5)

${(27^{\frac{5}{3}})}^{\frac{1}{5}}$

Step 1

Simplify the expression.

Multiply the exponents in ${(27^{\frac{5}{3}})}^{\frac{1}{5}}$ .

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

$27^{\frac{5}{3} \cdot \frac{1}{5}}$

Cancel the common factor of $5$ .

Cancel the common factor.

$27^{\frac{5}{3} \cdot \frac{1}{5}}$

Rewrite the expression.

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

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

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

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

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

Step 2

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$3^{1}$

Step 3

Evaluate the exponent.

$3$