Solve (x^-2)^4*x^10

$$( x ^ { - 2 } ) ^ { 4 } \cdot x ^ { 10 }$$

Evaluate

$$x^{2}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -2 and 4 to get -8.

$$x^{-8}x^{10}$$

To multiply powers of the same base, add their exponents. Add -8 and 10 to get 2.

$$x^{2}$$

Differentiate w.r.t. x

$$2x$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply -2 and 4 to get -8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{-8}x^{10})$$

To multiply powers of the same base, add their exponents. Add -8 and 10 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2})$$

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

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

Subtract 1 from 2.

$$2x^{1}$$

For any term t, t^{1}=t.

$$2x$$