Solve x^-6*x^-3/x^-8

$$\frac { x ^ { - 6 } \cdot x ^ { - 3 } } { x ^ { - 8 } }$$

Evaluate

$$\frac{1}{x}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -6 and -3 to get -9.

$$\frac{x^{-9}}{x^{-8}}$$

Rewrite x^{-8} as x^{-9}x. Cancel out x^{-9} in both numerator and denominator.

$$\frac{1}{x}$$

Differentiate w.r.t. x

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

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -6 and -3 to get -9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{-9}}{x^{-8}})$$

Rewrite x^{-8} as x^{-9}x. Cancel out x^{-9} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{x})$$

The derivative of ax^{n} is nax^{n-1}.

$$-x^{-1-1}$$

Subtract 1 from -1.

$$-x^{-2}$$