Solve (x^frac{3{8}})^16divx

$$( x ^ { \frac { 3 } { 8 } } ) ^ { 16 } \div x$$

Evaluate

$$x^{5}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply \frac{3}{8} and 16 to get 6.

$$\frac{x^{6}}{x}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 6 to get 5.

$$x^{5}$$

Differentiate w.r.t. x

$$5x^{4}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply \frac{3}{8} and 16 to get 6.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 6 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{5})$$

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

$$5x^{5-1}$$

Subtract 1 from 5.

$$5x^{4}$$