Algebra Examples

${(a^{\frac{1}{2}} b)}^{\frac{1}{2}} (a b^{\frac{1}{2}})$

Step 1

Remove parentheses.

${(a^{\frac{1}{2}} b)}^{\frac{1}{2}} a b^{\frac{1}{2}}$

Step 2

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

${(\sqrt{a^{1}} b)}^{\frac{1}{2}} a b^{\frac{1}{2}}$

Step 3

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\sqrt{{(\sqrt{a^{1}} b)}^{1}} a b^{\frac{1}{2}}$

Step 4

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\sqrt{{(\sqrt{a^{1}} b)}^{1}} a \sqrt{b^{1}}$

Step 5

Anything raised to $1$ is the base itself.

$\sqrt{{(\sqrt{a} b)}^{1}} a \sqrt{b^{1}}$

Step 6

Anything raised to $1$ is the base itself.

$\sqrt{\sqrt{a} b} a \sqrt{b^{1}}$

Step 7

Anything raised to $1$ is the base itself.

$\sqrt{\sqrt{a} b} a \sqrt{b}$