Solve (x^7/x^frac{2{3}})

$$( \frac { x ^ { 7 } } { x ^ { \frac { 2 } { 3 } } } )$$

Evaluate

$$x^{\frac{19}{3}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{x^{7}}{x^{\frac{2}{3}}}$$

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

$$x^{7-\frac{2}{3}}$$

Subtract \frac{2}{3} from 7.

$$x^{\frac{19}{3}}$$

Differentiate w.r.t. x

$$\frac{19x^{\frac{16}{3}}}{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{1}x^{7-\frac{2}{3}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{\frac{19}{3}})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$\frac{19}{3}x^{\frac{19}{3}-1}$$

Do the arithmetic.

$$\frac{19}{3}x^{\frac{16}{3}}$$