Solve {left(x^3right)}^-frac{1{3}}

$${ \left( { x }^{ 3 } \right) }^{ - \frac{ 1 }{ 3 } }$$

Evaluate

$$\frac{1}{x}$$

Steps for Raising Power to Another Power

Use the rules of exponents to simplify the expression.

$$\left(x^{3}\right)^{-\frac{1}{3}}$$

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

$$x^{3\left(-\frac{1}{3}\right)}$$

Multiply 3 times -\frac{1}{3}.

$$\frac{1}{x}$$

Differentiate w.r.t. x

$$-\frac{1}{x^{2}}$$

Steps Using Chain Rule

If F is the composition of two differentiable functions f\left(u\right) and u=g\left(x\right), that is, if F\left(x\right)=f\left(g\left(x\right)\right), then the derivative of F is the derivative of f with respect to u times the derivative of g with respect to x, that is, \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right).

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

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$-\frac{1}{3}\left(x^{3}\right)^{-\frac{4}{3}}\times 3x^{3-1}$$

Simplify.

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