Simplify 100^(1/2)-125^(1/3)

$100^{\frac{1}{2}} - 125^{\frac{1}{3}}$

Step 1

Simplify each term.

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

${(10^{2})}^{\frac{1}{2}} - 125^{\frac{1}{3}}$

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

$10^{2 (\frac{1}{2})} - 125^{\frac{1}{3}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$10^{2 (\frac{1}{2})} - 125^{\frac{1}{3}}$

Rewrite the expression.

$10^{1} - 125^{\frac{1}{3}}$

Evaluate the exponent.

$10 - 125^{\frac{1}{3}}$

Rewrite $125$ as $5^{3}$ .

$10 - {(5^{3})}^{\frac{1}{3}}$

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

$10 - 5^{3 (\frac{1}{3})}$

Cancel the common factor of $3$ .

Cancel the common factor.

$10 - 5^{3 (\frac{1}{3})}$

Rewrite the expression.

$10 - 5^{1}$

Evaluate the exponent.

$10 - 1 \cdot 5$

Multiply $- 1$ by $5$ .

$10 - 5$

Step 2

Subtract $5$ from $10$ .

$5$