Algebra Examples

$\frac{m^{\frac{2}{3}} \cdot m^{- \frac{1}{2}}}{m^{\frac{1}{6}}}$

Step 1

Multiply $m^{\frac{2}{3}}$ by $m^{- \frac{1}{2}}$ 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.

$\frac{m^{\frac{2}{3} - \frac{1}{2}}}{m^{\frac{1}{6}}}$

Step 1.2

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

$\frac{m^{\frac{2}{3} \cdot \frac{2}{2} - \frac{1}{2}}}{m^{\frac{1}{6}}}$

Step 1.3

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

$\frac{m^{\frac{2}{3} \cdot \frac{2}{2} - \frac{1}{2} \cdot \frac{3}{3}}}{m^{\frac{1}{6}}}$

Step 1.4

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

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Step 1.4.1

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

$\frac{m^{\frac{2 \cdot 2}{3 \cdot 2} - \frac{1}{2} \cdot \frac{3}{3}}}{m^{\frac{1}{6}}}$

Step 1.4.2

Multiply $3$ by $2$ .

$\frac{m^{\frac{2 \cdot 2}{6} - \frac{1}{2} \cdot \frac{3}{3}}}{m^{\frac{1}{6}}}$

Step 1.4.3

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

$\frac{m^{\frac{2 \cdot 2}{6} - \frac{3}{2 \cdot 3}}}{m^{\frac{1}{6}}}$

Step 1.4.4

Multiply $2$ by $3$ .

$\frac{m^{\frac{2 \cdot 2}{6} - \frac{3}{6}}}{m^{\frac{1}{6}}}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{m^{\frac{2 \cdot 2 - 3}{6}}}{m^{\frac{1}{6}}}$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $2$ by $2$ .

$\frac{m^{\frac{4 - 3}{6}}}{m^{\frac{1}{6}}}$

Step 1.6.2

Subtract $3$ from $4$ .

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

Step 2

Cancel the common factor.

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

Step 3

Rewrite the expression.

$1$