Simplify x^(-2/3)*x^(6/7)

$x^{- \frac{2}{3}} \cdot x^{\frac{6}{7}}$

Step 1

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

$x^{- \frac{2}{3} + \frac{6}{7}}$

Step 2

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

$x^{- \frac{2}{3} \cdot \frac{7}{7} + \frac{6}{7}}$

Step 3

To write $\frac{6}{7}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x^{- \frac{2}{3} \cdot \frac{7}{7} + \frac{6}{7} \cdot \frac{3}{3}}$

Step 4

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

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

$x^{- \frac{2 \cdot 7}{3 \cdot 7} + \frac{6}{7} \cdot \frac{3}{3}}$

Multiply $3$ by $7$ .

$x^{- \frac{2 \cdot 7}{21} + \frac{6}{7} \cdot \frac{3}{3}}$

Multiply $\frac{6}{7}$ by $\frac{3}{3}$ .

$x^{- \frac{2 \cdot 7}{21} + \frac{6 \cdot 3}{7 \cdot 3}}$

Multiply $7$ by $3$ .

$x^{- \frac{2 \cdot 7}{21} + \frac{6 \cdot 3}{21}}$

Step 5

Combine the numerators over the common denominator.

$x^{\frac{- 2 \cdot 7 + 6 \cdot 3}{21}}$

Step 6

Simplify the numerator.

Multiply $- 2$ by $7$ .

$x^{\frac{- 14 + 6 \cdot 3}{21}}$

Multiply $6$ by $3$ .

$x^{\frac{- 14 + 18}{21}}$

Add $- 14$ and $18$ .

$x^{\frac{4}{21}}$