Solve frac{q^frac{16{5}}}{q^frac{6{5}}}

$$\frac { q ^ { \frac { 16 } { 5 } } } { q ^ { \frac { 6 } { 5 } } }$$

Evaluate

$$q^{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{q^{\frac{16}{5}}}{q^{\frac{6}{5}}}$$

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

$$q^{\frac{16}{5}-\frac{6}{5}}$$

Subtract \frac{6}{5} from \frac{16}{5} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$q^{2}$$

Differentiate w.r.t. q

$$2q$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}q}(\frac{1}{1}q^{\frac{16}{5}-\frac{6}{5}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}q}(q^{2})$$

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}.

$$2q^{2-1}$$

Do the arithmetic.

$$2q^{1}$$

For any term t, t^{1}=t.

$$2q$$