Question

simplify.
$u^{\frac{2}{5}} \cdot u^{\frac{4}{7}}$
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 $u^{\frac{2}{5}} \cdot u^{\frac{4}{7}} = u^{\frac{2}{5}+\frac{4}{7}}$

Step2: Add the fractions

Find a common denominator (35) for the exponents:
$\frac{2}{5}+\frac{4}{7} = \frac{2\times7}{5\times7}+\frac{4\times5}{7\times5} = \frac{14}{35}+\frac{20}{35} = \frac{34}{35}$

Answer:

$u^{\frac{34}{35}}$