Solve (x^2)^3/x^4=

$$\frac { ( x ^ { 2 } ) ^ { 3 } } { x ^ { 4 } } =$$

Evaluate

$$x^{2}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Multiply 2 times 3.

$$x^{6}x^{4\left(-1\right)}$$

Multiply 4 times -1.

$$x^{6}x^{-4}$$

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

$$x^{6-4}$$

Add the exponents 6 and -4.

$$x^{2}$$

Differentiate w.r.t. x

$$2x$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{6}}{x^{4}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 6 to get 2.

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

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

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

Subtract 1 from 2.

$$2x^{1}$$

For any term t, t^{1}=t.

$$2x$$