Solve r^3r^-4/r^-2r^-5=

$$\frac { r ^ { 3 } r ^ { - 4 } } { r ^ { - 2 } r ^ { - 5 } } =$$

Evaluate

$$r^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and -4 to get -1.

$$\frac{r^{-1}}{r^{-2}r^{-5}}$$

To multiply powers of the same base, add their exponents. Add -2 and -5 to get -7.

$$\frac{r^{-1}}{r^{-7}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -7 from -1 to get 6.

$$r^{6}$$

Differentiate w.r.t. r

$$6r^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and -4 to get -1.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{r^{-1}}{r^{-2}r^{-5}})$$

To multiply powers of the same base, add their exponents. Add -2 and -5 to get -7.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{r^{-1}}{r^{-7}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -7 from -1 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}r}(r^{6})$$

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

$$6r^{6-1}$$

Subtract 1 from 6.

$$6r^{5}$$