Solve (-4x^-3)^0*(-4x^3)^2

$$( - 4 x ^ { - 3 } ) ^ { 0 } \times ( - 4 x ^ { 3 } ) ^ { 2 }$$

Evaluate

$$16x^{6}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(-4x^{-3}\right)^{0}\left(-4x^{3}\right)^{2}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$\left(-4\right)^{0}\left(x^{-3}\right)^{0}\left(-4\right)^{2}\left(x^{3}\right)^{2}$$

Use the Commutative Property of Multiplication.

$$\left(-4\right)^{0}\left(-4\right)^{2}\left(x^{-3}\right)^{0}\left(x^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents.

$$\left(-4\right)^{0}\left(-4\right)^{2}x^{0}x^{3\times 2}$$

Multiply 3 times 2.

$$\left(-4\right)^{0}\left(-4\right)^{2}x^{0}x^{6}$$

To multiply powers of the same base, add their exponents.

$$\left(-4\right)^{0}\left(-4\right)^{2}x^{6}$$

To multiply powers of the same base, add their exponents.

$$\left(-4\right)^{2}x^{6}$$

Differentiate w.r.t. x

$$96x^{5}$$

Steps Using Definition of a Derivative

Calculate -4x^{-3} to the power of 0 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(1\left(-4x^{3}\right)^{2})$$

Expand \left(-4x^{3}\right)^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(1\left(-4\right)^{2}\left(x^{3}\right)^{2})$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(1\left(-4\right)^{2}x^{6})$$

Calculate -4 to the power of 2 and get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(1\times 16x^{6})$$

Multiply 1 and 16 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(16x^{6})$$

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

$$6\times 16x^{6-1}$$

Multiply 6 times 16.

$$96x^{6-1}$$

Subtract 1 from 6.

$$96x^{5}$$