Solve ((x^-1)^3)^2

$$( ( x ^ { - 1 } ) ^ { 3 } ) ^ { 2 }$$

Evaluate

$$\frac{1}{x^{6}}$$

Steps for Raising Power to Another Power

To raise a power to another power, multiply the exponents. Multiply -1 and 3 to get -3.

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

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

$$x^{-3\times 2}$$

Multiply -3 times 2.

$$\frac{1}{x^{6}}$$

Differentiate w.r.t. x

$$-\frac{6}{x^{7}}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply -1 and 3 to get -3.

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

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

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

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

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

Subtract 1 from -6.

$$-6x^{-7}$$