Simplify m^(4/9)*m^(1/4)

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

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

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

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

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

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

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

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

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

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

Multiply $9$ by $4$ .

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

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

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

Multiply $4$ by $9$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $4$ by $4$ .

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

Add $16$ and $9$ .

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