Simplify (x^(2/3))/(x^(4/9))

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

Step 1

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

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

Step 2

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

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

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

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

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

Multiply $\frac{2}{3}$ by $\frac{3}{3}$ .

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

Multiply $3$ by $3$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $3$ .

$x^{\frac{6 - 4}{9}}$

Subtract $4$ from $6$ .

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