Algebra Examples

$\frac{a^{\frac{2}{3}} b^{\frac{1}{2}}}{b^{\frac{3}{2}} \cdot \sqrt[3]{a}}$

Step 1

Reduce the expression $\frac{a^{\frac{2}{3}} b^{\frac{1}{2}}}{b^{\frac{3}{2}} \cdot \sqrt[3]{a}}$ by cancelling the common factors.

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Step 1.1

Factor $b^{\frac{3}{2}}$ out of $a^{\frac{2}{3}} b^{\frac{1}{2}}$ .

$\frac{b^{\frac{3}{2}} (a^{\frac{2}{3}} b^{\frac{- 2}{2}})}{b^{\frac{3}{2}} \cdot \sqrt[3]{a}}$

Step 1.2

Factor $b^{\frac{3}{2}}$ out of $b^{\frac{3}{2}} \cdot \sqrt[3]{a}$ .

$\frac{b^{\frac{3}{2}} (a^{\frac{2}{3}} b^{\frac{- 2}{2}})}{b^{\frac{3}{2}} (\sqrt[3]{a})}$

Step 1.3

Cancel the common factor.

$\frac{b^{\frac{3}{2}} (a^{\frac{2}{3}} b^{\frac{- 2}{2}})}{b^{\frac{3}{2}} \sqrt[3]{a}}$

Step 1.4

Rewrite the expression.

$\frac{a^{\frac{2}{3}} b^{\frac{- 2}{2}}}{\sqrt[3]{a}}$

Step 2

Reduce the expression $\frac{- 2}{2}$ by cancelling the common factors.

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Step 2.1

Factor $2$ out of $- 2$ .

$\frac{a^{\frac{2}{3}} b^{\frac{2 \cdot - 1}{2}}}{\sqrt[3]{a}}$

Step 2.2

Factor $2$ out of $2$ .

$\frac{a^{\frac{2}{3}} b^{\frac{2 \cdot - 1}{2 (1)}}}{\sqrt[3]{a}}$

Step 2.3

Cancel the common factor.

$\frac{a^{\frac{2}{3}} b^{\frac{2 \cdot - 1}{2 \cdot 1}}}{\sqrt[3]{a}}$

Step 2.4

Rewrite the expression.

$\frac{a^{\frac{2}{3}} b^{\frac{- 1}{1}}}{\sqrt[3]{a}}$

Step 3

Divide $- 1$ by $1$ .

$\frac{a^{\frac{2}{3}} b^{- 1}}{\sqrt[3]{a}}$

Step 4

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

$\frac{\sqrt[3]{a^{2}} b^{- 1}}{\sqrt[3]{a}}$