Evaluate 5^(1/3)*25^(1/3)

$5^{\frac{1}{3}} \cdot 25^{\frac{1}{3}}$

Step 1

Multiply $5^{\frac{1}{3}} \cdot 25^{\frac{1}{3}}$ .

Rewrite $25$ as $5^{2}$ .

$5^{\frac{1}{3}} \cdot {(5^{2})}^{\frac{1}{3}}$

Multiply the exponents in ${(5^{2})}^{\frac{1}{3}}$ .

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

$5^{\frac{1}{3}} \cdot 5^{2 (\frac{1}{3})}$

Combine $2$ and $\frac{1}{3}$ .

$5^{\frac{1}{3}} \cdot 5^{\frac{2}{3}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$5^{\frac{1}{3} + \frac{2}{3}}$

Combine the numerators over the common denominator.

$5^{\frac{1 + 2}{3}}$

Add $1$ and $2$ .

$5^{\frac{3}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$5^{\frac{3}{3}}$

Rewrite the expression.

$5^{1}$

Step 2

Evaluate the exponent.

$5$