Solve x^-8*x^5/x^-6

$$\frac { x ^ { - 8 } \cdot x ^ { 5 } } { x ^ { - 6 } }$$

Evaluate

$$x^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -8 and 5 to get -3.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -6 from -3 to get 3.

$$x^{3}$$

Differentiate w.r.t. x

$$3x^{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -8 and 5 to get -3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{-3}}{x^{-6}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -6 from -3 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3})$$

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

$$3x^{3-1}$$

Subtract 1 from 3.

$$3x^{2}$$