Basic Math Examples

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

Step 1

Multiply $y^{\frac{1}{3}}$ by $y^{\frac{3}{6}}$ by adding the exponents.

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Step 1.1

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

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

Step 1.2

Cancel the common factor of $3$ and $6$ .

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Step 1.2.1

Factor $3$ out of $3$ .

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

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $3$ out of $6$ .

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

Step 1.2.2.2

Cancel the common factor.

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

Step 1.2.2.3

Rewrite the expression.

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

Step 1.3

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 1.4

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 1.5

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.5.1

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

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

Step 1.5.2

Multiply $3$ by $2$ .

$\frac{y^{\frac{2}{6} + \frac{1}{2} \cdot \frac{3}{3}}}{y}$

Step 1.5.3

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$\frac{y^{\frac{2}{6} + \frac{3}{2 \cdot 3}}}{y}$

Step 1.5.4

Multiply $2$ by $3$ .

$\frac{y^{\frac{2}{6} + \frac{3}{6}}}{y}$

Step 1.6

Combine the numerators over the common denominator.

$\frac{y^{\frac{2 + 3}{6}}}{y}$

Step 1.7

Add $2$ and $3$ .

$\frac{y^{\frac{5}{6}}}{y}$

Step 2

Move $y^{\frac{5}{6}}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

$\frac{1}{y \cdot y^{- \frac{5}{6}}}$

Step 3

Multiply $y$ by $y^{- \frac{5}{6}}$ by adding the exponents.

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Step 3.1

Multiply $y$ by $y^{- \frac{5}{6}}$ .

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Step 3.1.1

Raise $y$ to the power of $1$ .

$\frac{1}{y^{1} y^{- \frac{5}{6}}}$

Step 3.1.2

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

$\frac{1}{y^{1 - \frac{5}{6}}}$

Step 3.2

Write $1$ as a fraction with a common denominator.

$\frac{1}{y^{\frac{6}{6} - \frac{5}{6}}}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{1}{y^{\frac{6 - 5}{6}}}$

Step 3.4

Subtract $5$ from $6$ .

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