Solve (64x^9)^1/3

$$( 64 x ^ { 9 } ) ^ { 1 / 3 }$$

Evaluate

$$4x^{3}$$

Steps for Raising Power to Another Power

Use the rules of exponents to simplify the expression.

$$\sqrt[3]{64x^{9}}$$

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

$$\sqrt[3]{64}\sqrt[3]{x^{9}}$$

Raise 64 to the power \frac{1}{3}.

$$4\sqrt[3]{x^{9}}$$

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

$$4x^{9\times \frac{1}{3}}$$

Multiply 9 times \frac{1}{3}.

$$4x^{3}$$

Differentiate w.r.t. x

$$12x^{2}$$

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).

$$\frac{1}{3}\times \left(64x^{9}\right)^{\frac{1}{3}-1}\frac{\mathrm{d}}{\mathrm{d}x}(64x^{9})$$

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}.

$$\frac{1}{3}\times \left(64x^{9}\right)^{-\frac{2}{3}}\times 9\times 64x^{9-1}$$

Simplify.

$$192x^{8}\times \left(64x^{9}\right)^{-\frac{2}{3}}$$