Solve (2x^-3)(x^2)^4

$$( 2 x ^ { - 3 } ) ( x ^ { 2 } ) ^ { 4 }$$

Evaluate

$$2x^{5}$$

Solution Steps

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

$$2x^{-3}x^{8}$$

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

$$2x^{5}$$

Differentiate w.r.t. x

$$10x^{4}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{-3}x^{8})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{5})$$

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

$$5\times 2x^{5-1}$$

Multiply 5 times 2.

$$10x^{5-1}$$

Subtract 1 from 5.

$$10x^{4}$$