Algebra Examples

$\frac{12 y^{\frac{1}{3}}}{4 y^{\frac{1}{2}}}$

Step 1

Reduce the expression $\frac{12 y^{\frac{1}{3}}}{4 y^{\frac{1}{2}}}$ by cancelling the common factors.

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Step 1.1

Factor $4$ out of $12 y^{\frac{1}{3}}$ .

$\frac{4 (3 y^{\frac{1}{3}})}{4 y^{\frac{1}{2}}}$

Step 1.2

Factor $4$ out of $4 y^{\frac{1}{2}}$ .

$\frac{4 (3 y^{\frac{1}{3}})}{4 (y^{\frac{1}{2}})}$

Step 1.3

Cancel the common factor.

$\frac{4 (3 y^{\frac{1}{3}})}{4 y^{\frac{1}{2}}}$

Step 1.4

Rewrite the expression.

$\frac{3 y^{\frac{1}{3}}}{y^{\frac{1}{2}}}$

Step 2

Reduce the expression $\frac{3 y^{\frac{1}{3}}}{y^{\frac{1}{2}}}$ by cancelling the common factors.

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Step 2.1

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

$\frac{y^{\frac{1}{2}} (3 y^{- \frac{1}{6}})}{y^{\frac{1}{2}}}$

Step 2.2

Multiply by $1$ .

$\frac{y^{\frac{1}{2}} (3 y^{- \frac{1}{6}})}{y^{\frac{1}{2}} \cdot 1}$

Step 2.3

Cancel the common factor.

$\frac{y^{\frac{1}{2}} (3 y^{- \frac{1}{6}})}{y^{\frac{1}{2}} \cdot 1}$

Step 2.4

Rewrite the expression.

$\frac{3 y^{- \frac{1}{6}}}{1}$

Step 3

Divide $3 y^{- \frac{1}{6}}$ by $1$ .

$3 y^{- \frac{1}{6}}$

Step 4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$3 \frac{1}{y^{\frac{1}{6}}}$

Step 5

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

$3 \frac{1}{\sqrt[6]{y^{1}}}$

Step 6

Anything raised to $1$ is the base itself.

$3 \frac{1}{\sqrt[6]{y}}$