Solve (j^8)^2/(j^5)^2

$$\frac { ( j ^ { 8 } ) ^ { 2 } } { ( j ^ { 5 } ) ^ { 2 } }$$

Evaluate

$$j^{6}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 8 and 2 to get 16.

$$\frac{j^{16}}{\left(j^{5}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{j^{16}}{j^{10}}$$

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

$$j^{6}$$

Differentiate w.r.t. j

$$6j^{5}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 8 and 2 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}j}(\frac{j^{16}}{\left(j^{5}\right)^{2}})$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}j}(\frac{j^{16}}{j^{10}})$$

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

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

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

$$6j^{6-1}$$

Subtract 1 from 6.

$$6j^{5}$$