Solve (x^-5)^-2*x^-7

$$( x ^ { - 5 } ) ^ { - 2 } \cdot x ^ { - 7 }$$

Evaluate

$$x^{3}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -5 and -2 to get 10.

$$x^{10}x^{-7}$$

To multiply powers of the same base, add their exponents. Add 10 and -7 to get 3.

$$x^{3}$$

Differentiate w.r.t. x

$$3x^{2}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply -5 and -2 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{10}x^{-7})$$

To multiply powers of the same base, add their exponents. Add 10 and -7 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.

$$3x^{2}$$