Solve q^12*q^4/q^6

$$\frac { q ^ { 12 } \times q ^ { 4 } } { q ^ { 6 } }$$

Evaluate

$$q^{10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 12 and 4 to get 16.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 16 to get 10.

$$q^{10}$$

Differentiate w.r.t. q

$$10q^{9}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 12 and 4 to get 16.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 16 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}q}(q^{10})$$

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

$$10q^{10-1}$$

Subtract 1 from 10.

$$10q^{9}$$