Question

simplify.
$u^{\frac{1}{3}} \cdot u^{\frac{7}{9}}$
assume that the variable represents a positive real number.

Explanation:

Step1: Apply exponent product rule

When multiplying terms with the same base, add exponents: $u^a \cdot u^b = u^{a+b}$
So $u^{\frac{1}{3}} \cdot u^{\frac{7}{9}} = u^{\frac{1}{3} + \frac{7}{9}}$

Step2: Add the fractions

Convert $\frac{1}{3}$ to a fraction with denominator 9: $\frac{1}{3} = \frac{3}{9}$
$\frac{3}{9} + \frac{7}{9} = \frac{3+7}{9} = \frac{10}{9}$

Answer:

$u^{\frac{10}{9}}$