Solve 8(a^4)^2:(a^2)

$$8 ( a ^ { 4 } ) ^ { 2 } : ( a ^ { 2 } )$$

Evaluate

$$8a^{6}$$

Solution Steps

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

$$\frac{8a^{8}}{a^{2}}$$

Cancel out a^{2} in both numerator and denominator.

$$8a^{6}$$

Differentiate w.r.t. a

$$48a^{5}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{8a^{8}}{a^{2}})$$

Cancel out a^{2} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(8a^{6})$$

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

$$6\times 8a^{6-1}$$

Multiply 6 times 8.

$$48a^{6-1}$$

Subtract 1 from 6.

$$48a^{5}$$