Simplify 9/(9^(-4/5))

$\frac{9}{9^{- \frac{4}{5}}}$

Step 1

Move $9^{- \frac{4}{5}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$9 \cdot 9^{\frac{4}{5}}$

Step 2

Multiply $9$ by $9^{\frac{4}{5}}$ by adding the exponents.

Multiply $9$ by $9^{\frac{4}{5}}$ .

Raise $9$ to the power of $1$ .

$9^{1} \cdot 9^{\frac{4}{5}}$

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

$9^{1 + \frac{4}{5}}$

Write $1$ as a fraction with a common denominator.

$9^{\frac{5}{5} + \frac{4}{5}}$

Combine the numerators over the common denominator.

$9^{\frac{5 + 4}{5}}$

Add $5$ and $4$ .

$9^{\frac{9}{5}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$9^{\frac{9}{5}}$

Decimal Form:

$52.19591521 \dots$