Solve (x^-3)^4*4x^13

$$( x ^ { - 3 } ) ^ { 4 } \cdot 4 x ^ { 13 }$$

Evaluate

$$4x$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -3 and 4 to get -12.

$$x^{-12}\times 4x^{13}$$

To multiply powers of the same base, add their exponents. Add -12 and 13 to get 1.

$$x^{1}\times 4$$

Calculate x to the power of 1 and get x.

$$x\times 4$$

Differentiate w.r.t. x

$$4$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply -3 and 4 to get -12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{-12}\times 4x^{13})$$

To multiply powers of the same base, add their exponents. Add -12 and 13 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}\times 4)$$

Calculate x to the power of 1 and get x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times 4)$$

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

$$4x^{1-1}$$

Subtract 1 from 1.

$$4x^{0}$$

For any term t except 0, t^{0}=1.

$$4\times 1$$

For any term t, t\times 1=t and 1t=t.

$$4$$