Simplify (x^(-a))/(x^(-b)x^c)

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

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

$\frac{x^{- a}}{x^{- b + c}}$

Cancel the common factor of $x^{- a}$ and $x^{- b + c}$ .

Factor $x^{- b + c}$ out of $x^{- a}$ .

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

Cancel the common factors.

Multiply by $1$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $x^{- a - (- b + c)}$ by $1$ .

$x^{- a - (- b + c)}$

Simplify each term.

Apply the distributive property.

$x^{- a - - b - c}$

Multiply $- - b$ .

Multiply $- 1$ by $- 1$ .

$x^{- a + 1 b - c}$

Multiply $b$ by $1$ .

$x^{- a + b - c}$