Simplify the Radical Expression (x^(8/9))(x^(1/3))

$(x^{\frac{8}{9}}) (x^{\frac{1}{3}})$

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

$x^{\frac{8}{9} + \frac{1}{3}}$

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x^{\frac{8}{9} + \frac{1}{3} \cdot \frac{3}{3}}$

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

Multiply $\frac{1}{3}$ by $\frac{3}{3}$ .

$x^{\frac{8}{9} + \frac{3}{3 \cdot 3}}$

Multiply $3$ by $3$ .

$x^{\frac{8}{9} + \frac{3}{9}}$

Combine the numerators over the common denominator.

$x^{\frac{8 + 3}{9}}$

Add $8$ and $3$ .

$x^{\frac{11}{9}}$