Simplify (c^(2/9))(c^(4/3))

$(c^{\frac{2}{9}}) (c^{\frac{4}{3}})$

Step 1

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

$c^{\frac{2}{9} + \frac{4}{3}}$

Step 2

To write $\frac{4}{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$c^{\frac{2}{9} + \frac{4}{3} \cdot \frac{3}{3}}$

Step 3

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4}{3}$ by $\frac{3}{3}$ .

$c^{\frac{2}{9} + \frac{4 \cdot 3}{3 \cdot 3}}$

Multiply $3$ by $3$ .

$c^{\frac{2}{9} + \frac{4 \cdot 3}{9}}$

Step 4

Combine the numerators over the common denominator.

$c^{\frac{2 + 4 \cdot 3}{9}}$

Step 5

Simplify the numerator.

Multiply $4$ by $3$ .

$c^{\frac{2 + 12}{9}}$

Add $2$ and $12$ .

$c^{\frac{14}{9}}$