Simplify (9^(1/4))^(7/2)

${(9^{\frac{1}{4}})}^{\frac{7}{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$9^{\frac{1}{4} \cdot \frac{7}{2}}$

Multiply $\frac{1}{4} \cdot \frac{7}{2}$ .

Multiply $\frac{1}{4}$ by $\frac{7}{2}$ .

$9^{\frac{7}{4 \cdot 2}}$

Multiply $4$ by $2$ .

$9^{\frac{7}{8}}$

The result can be shown in multiple forms.

Exact Form:

$9^{\frac{7}{8}}$

Decimal Form:

$6.83852117 \dots$