Solve (36x^2)^2/6x^-frac{1{3}}

$$\frac { ( 36 x ^ { 2 } ) ^ { 2 } } { 6 x ^ { - \frac { 1 } { 3 } } }$$

Evaluate

$$216x^{\frac{13}{3}}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(36x^{2}\right)^{2}\times \frac{1}{6x^{-\frac{1}{3}}}$$

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

$$36^{2}\left(x^{2}\right)^{2}\times \frac{1}{6}\times \frac{1}{x^{-\frac{1}{3}}}$$

Use the Commutative Property of Multiplication.

$$36^{2}\times \frac{1}{6}\left(x^{2}\right)^{2}\times \frac{1}{x^{-\frac{1}{3}}}$$

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

$$36^{2}\times \frac{1}{6}x^{2\times 2}x^{-\frac{1}{3}\left(-1\right)}$$

Multiply 2 times 2.

$$36^{2}\times \frac{1}{6}x^{4}x^{-\frac{1}{3}\left(-1\right)}$$

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

$$36^{2}\times \frac{1}{6}x^{4}\sqrt[3]{x}$$

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

$$36^{2}\times \frac{1}{6}x^{4+\frac{1}{3}}$$

Add the exponents 4 and \frac{1}{3}.

$$36^{2}\times \frac{1}{6}x^{\frac{13}{3}}$$

Raise 36 to the power 2.

$$1296\times \frac{1}{6}x^{\frac{13}{3}}$$

Multiply 1296 times \frac{1}{6}.

$$216x^{\frac{13}{3}}$$

Differentiate w.r.t. x

$$936x^{\frac{10}{3}}$$

Steps Using Definition of a Derivative

Expand \left(36x^{2}\right)^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{36^{2}\left(x^{2}\right)^{2}}{6x^{-\frac{1}{3}}})$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{36^{2}x^{4}}{6x^{-\frac{1}{3}}})$$

Calculate 36 to the power of 2 and get 1296.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1296x^{4}}{6x^{-\frac{1}{3}}})$$

Cancel out 6 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{216x^{4}}{x^{-\frac{1}{3}}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}x}(216x^{\frac{13}{3}})$$

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

$$\frac{13}{3}\times 216x^{\frac{13}{3}-1}$$

Multiply \frac{13}{3} times 216.

$$936x^{\frac{13}{3}-1}$$

Subtract 1 from \frac{13}{3}.

$$936x^{\frac{10}{3}}$$