Solve q^9/q^-8*q^-3

$$\frac { q ^ { 9 } } { q ^ { - 8 } \cdot q ^ { - 3 } }$$

Evaluate

$$q^{20}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -8 and -3 to get -11.

$$\frac{q^{9}}{q^{-11}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -11 from 9 to get 20.

$$q^{20}$$

Differentiate w.r.t. q

$$20q^{19}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -8 and -3 to get -11.

$$\frac{\mathrm{d}}{\mathrm{d}q}(\frac{q^{9}}{q^{-11}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -11 from 9 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}q}(q^{20})$$

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

$$20q^{20-1}$$

Subtract 1 from 20.

$$20q^{19}$$