Solve 16{left(x^8right)}^-frac{1{4}}

$$16 { \left( { x }^{ 8 } \right) }^{ - \frac{ 1 }{ 4 } }$$

Differentiate w.r.t. x

$$-\frac{32}{x^{3}}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 8 and -\frac{1}{4} to get -2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(16x^{-2})$$

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

$$-2\times 16x^{-2-1}$$

Multiply -2 times 16.

$$-32x^{-2-1}$$

Subtract 1 from -2.

$$-32x^{-3}$$

Evaluate

$$\frac{16}{x^{2}}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 8 and -\frac{1}{4} to get -2.

$$16x^{-2}$$