Solve (x^4)^4/x^6

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

Evaluate

$$x^{10}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Multiply 4 times 4.

$$x^{16}x^{6\left(-1\right)}$$

Multiply 6 times -1.

$$x^{16}x^{-6}$$

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

$$x^{16-6}$$

Add the exponents 16 and -6.

$$x^{10}$$

Differentiate w.r.t. x

$$10x^{9}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{16}}{x^{6}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 16 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{10})$$

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

$$10x^{10-1}$$

Subtract 1 from 10.

$$10x^{9}$$