Evaluate (9^(4/3))/(9^(2/3))

$\frac{9^{\frac{4}{3}}}{9^{\frac{2}{3}}}$

Step 1

Move $9^{\frac{2}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$9^{\frac{4}{3}} \cdot 9^{- \frac{2}{3}}$

Step 2

Multiply $9^{\frac{4}{3}}$ by $9^{- \frac{2}{3}}$ by adding the exponents.

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

$9^{\frac{4}{3} - \frac{2}{3}}$

Combine the numerators over the common denominator.

$9^{\frac{4 - 2}{3}}$

Subtract $2$ from $4$ .

$9^{\frac{2}{3}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$9^{\frac{2}{3}}$

Decimal Form:

$4.32674871 \dots$