Question

simplify.
\\( x^{\frac{4}{9}} \cdot x^{\frac{2}{3}} \\)
assume that the variable represents a positive real number.

Explanation:

Step1: Apply exponent product rule

When multiplying terms with the same base, add exponents: $x^a \cdot x^b = x^{a+b}$

Step2: Convert to common denominator

Rewrite $\frac{2}{3}$ as $\frac{6}{9}$ to add fractions:
$\frac{4}{9} + \frac{2}{3} = \frac{4}{9} + \frac{6}{9}$

Step3: Add the fractions

$\frac{4 + 6}{9} = \frac{10}{9}$

Answer:

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