Solve w^frac{6{5}}divw^frac{11{5}}

$$w ^ { \frac { 6 } { 5 } } \div w ^ { \frac { 11 } { 5 } }$$

Evaluate

$$\frac{1}{w}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{w^{\frac{6}{5}}}{w^{\frac{11}{5}}}$$

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

$$w^{\frac{6}{5}-\frac{11}{5}}$$

Subtract \frac{11}{5} from \frac{6}{5} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$\frac{1}{w}$$

Differentiate w.r.t. w

$$-\frac{1}{w^{2}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{1}{1}w^{\frac{6}{5}-\frac{11}{5}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{1}{w})$$

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}.

$$-w^{-1-1}$$

Do the arithmetic.

$$-w^{-2}$$