Algebra Examples

$m^{\frac{4}{9}} \times m^{\frac{1}{4}}$

Step 1

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

$m^{\frac{4}{9} + \frac{1}{4}}$

Step 2

To write $\frac{4}{9}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$m^{\frac{4}{9} \cdot \frac{4}{4} + \frac{1}{4}}$

Step 3

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$m^{\frac{4}{9} \cdot \frac{4}{4} + \frac{1}{4} \cdot \frac{9}{9}}$

Step 4

Write each expression with a common denominator of $36$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{4}{9}$ by $\frac{4}{4}$ .

$m^{\frac{4 \cdot 4}{9 \cdot 4} + \frac{1}{4} \cdot \frac{9}{9}}$

Step 4.2

Multiply $9$ by $4$ .

$m^{\frac{4 \cdot 4}{36} + \frac{1}{4} \cdot \frac{9}{9}}$

Step 4.3

Multiply $\frac{1}{4}$ by $\frac{9}{9}$ .

$m^{\frac{4 \cdot 4}{36} + \frac{9}{4 \cdot 9}}$

Step 4.4

Multiply $4$ by $9$ .

$m^{\frac{4 \cdot 4}{36} + \frac{9}{36}}$

Step 5

Combine the numerators over the common denominator.

$m^{\frac{4 \cdot 4 + 9}{36}}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $4$ by $4$ .

$m^{\frac{16 + 9}{36}}$

Step 6.2

Add $16$ and $9$ .

$m^{\frac{25}{36}}$