Solve (d^{2})^{2}(r^-6)^5(d^4)^2

$$( d ^ { 2 } ) ^ { 2 } ( r ^ { - 6 } ) ^ { 5 } ( d ^ { 4 } ) ^ { 2 }$$

Evaluate

$$\frac{d^{12}}{r^{30}}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$d^{4}\left(r^{-6}\right)^{5}\left(d^{4}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply -6 and 5 to get -30.

$$d^{4}r^{-30}\left(d^{4}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$d^{4}r^{-30}d^{8}$$

To multiply powers of the same base, add their exponents. Add 4 and 8 to get 12.

$$d^{12}r^{-30}$$

Differentiate w.r.t. r

$$-\frac{30d^{12}}{r^{31}}$$