Simplify (x^(4/7))/(x^(2/3))

$\frac{x^{\frac{4}{7}}}{x^{\frac{2}{3}}}$

Step 1

Move $x^{\frac{4}{7}}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

$\frac{1}{x^{\frac{2}{3}} x^{- \frac{4}{7}}}$

Step 2

Multiply $x^{\frac{2}{3}}$ by $x^{- \frac{4}{7}}$ by adding the exponents.

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

$\frac{1}{x^{\frac{2}{3} - \frac{4}{7}}}$

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{1}{x^{\frac{2}{3} \cdot \frac{7}{7} - \frac{4}{7}}}$

To write $- \frac{4}{7}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{x^{\frac{2}{3} \cdot \frac{7}{7} - \frac{4}{7} \cdot \frac{3}{3}}}$

Write each expression with a common denominator of $21$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{3}$ by $\frac{7}{7}$ .

$\frac{1}{x^{\frac{2 \cdot 7}{3 \cdot 7} - \frac{4}{7} \cdot \frac{3}{3}}}$

Multiply $3$ by $7$ .

$\frac{1}{x^{\frac{2 \cdot 7}{21} - \frac{4}{7} \cdot \frac{3}{3}}}$

Multiply $\frac{4}{7}$ by $\frac{3}{3}$ .

$\frac{1}{x^{\frac{2 \cdot 7}{21} - \frac{4 \cdot 3}{7 \cdot 3}}}$

Multiply $7$ by $3$ .

$\frac{1}{x^{\frac{2 \cdot 7}{21} - \frac{4 \cdot 3}{21}}}$

Combine the numerators over the common denominator.

$\frac{1}{x^{\frac{2 \cdot 7 - 4 \cdot 3}{21}}}$

Simplify the numerator.

Multiply $2$ by $7$ .

$\frac{1}{x^{\frac{14 - 4 \cdot 3}{21}}}$

Multiply $- 4$ by $3$ .

$\frac{1}{x^{\frac{14 - 12}{21}}}$

Subtract $12$ from $14$ .

$\frac{1}{x^{\frac{2}{21}}}$