Solve (8x)^frac{5{3}}

$$( 8 x ) ^ { \frac { 5 } { 3 } }$$

Evaluate

$$32x^{\frac{5}{3}}$$

Solution Steps

Expand \left(8x\right)^{\frac{5}{3}}.

$$8^{\frac{5}{3}}x^{\frac{5}{3}}$$

Calculate 8 to the power of \frac{5}{3} and get 32.

$$32x^{\frac{5}{3}}$$

Differentiate w.r.t. x

$$\frac{160x^{\frac{2}{3}}}{3}$$

Steps Using Definition of a Derivative

Expand \left(8x\right)^{\frac{5}{3}}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8^{\frac{5}{3}}x^{\frac{5}{3}})$$

Calculate 8 to the power of \frac{5}{3} and get 32.

$$\frac{\mathrm{d}}{\mathrm{d}x}(32x^{\frac{5}{3}})$$

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

$$\frac{5}{3}\times 32x^{\frac{5}{3}-1}$$

Multiply \frac{5}{3} times 32.

$$\frac{160}{3}x^{\frac{5}{3}-1}$$

Subtract 1 from \frac{5}{3}.

$$\frac{160}{3}x^{\frac{2}{3}}$$