Simplify (64^(5/9)*64^(2/9))/(4^(3/4))

$\frac{64^{\frac{5}{9}} \cdot 64^{\frac{2}{9}}}{4^{\frac{3}{4}}}$

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

$\frac{64^{\frac{5}{9} + \frac{2}{9}}}{4^{\frac{3}{4}}}$

Combine the numerators over the common denominator.

$\frac{64^{\frac{5 + 2}{9}}}{4^{\frac{3}{4}}}$

Add $5$ and $2$ .

$\frac{64^{\frac{7}{9}}}{4^{\frac{3}{4}}}$

The result can be shown in multiple forms.

Exact Form:

$\frac{64^{\frac{7}{9}}}{4^{\frac{3}{4}}}$

Decimal Form:

$8.97969638 \dots$