Evaluate 10^(1/3)*100^(1/3)

$10^{\frac{1}{3}} \cdot 100^{\frac{1}{3}}$

Step 1

Multiply $10^{\frac{1}{3}} \cdot 100^{\frac{1}{3}}$ .

Rewrite $100$ as $10^{2}$ .

$10^{\frac{1}{3}} \cdot {(10^{2})}^{\frac{1}{3}}$

Multiply the exponents in ${(10^{2})}^{\frac{1}{3}}$ .

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

$10^{\frac{1}{3}} \cdot 10^{2 (\frac{1}{3})}$

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

$10^{\frac{1}{3}} \cdot 10^{\frac{2}{3}}$

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

$10^{\frac{1}{3} + \frac{2}{3}}$

Combine the numerators over the common denominator.

$10^{\frac{1 + 2}{3}}$

Add $1$ and $2$ .

$10^{\frac{3}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$10^{\frac{3}{3}}$

Rewrite the expression.

$10^{1}$

Step 2

Evaluate the exponent.

$10$