Calculus Examples

${(x^{- \frac{b}{a}})}^{- \frac{a}{b}}$

Step 1

Multiply the exponents in ${(x^{- \frac{b}{a}})}^{- \frac{a}{b}}$ .

Tap for more steps...

Step 1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{- \frac{b}{a} (- \frac{a}{b})}$

Step 1.2

Cancel the common factor of $b$ .

Tap for more steps...

Step 1.2.1

Move the leading negative in $- \frac{b}{a}$ into the numerator.

$x^{\frac{- b}{a} (- \frac{a}{b})}$

Step 1.2.2

Move the leading negative in $- \frac{a}{b}$ into the numerator.

$x^{\frac{- b}{a} \cdot \frac{- a}{b}}$

Step 1.2.3

Factor $b$ out of $- b$ .

$x^{\frac{b \cdot - 1}{a} \cdot \frac{- a}{b}}$

Step 1.2.4

Cancel the common factor.

$x^{\frac{b \cdot - 1}{a} \cdot \frac{- a}{b}}$

Step 1.2.5

Rewrite the expression.

$x^{\frac{- 1}{a} (- a)}$

Step 1.3

Cancel the common factor of $a$ .

Tap for more steps...

Step 1.3.1

Factor $a$ out of $- a$ .

$x^{\frac{- 1}{a} (a \cdot - 1)}$

Step 1.3.2

Cancel the common factor.

$x^{\frac{- 1}{a} (a \cdot - 1)}$

Step 1.3.3

Rewrite the expression.

$x^{- - 1}$

Step 1.4

Multiply $- 1$ by $- 1$ .

$x^{1}$

Step 2

Simplify.

$x$