Solve left(a^8right)^2diva^8

$${ \left( { a }^{ 8 } \right) }^{ 2 } \div { a }^{ 8 }$$

Evaluate

$$a^{8}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(a^{8}\right)^{2}\times \frac{1}{a^{8}}$$

To raise a power to another power, multiply the exponents.

$$a^{8\times 2}a^{8\left(-1\right)}$$

Multiply 8 times 2.

$$a^{16}a^{8\left(-1\right)}$$

Multiply 8 times -1.

$$a^{16}a^{-8}$$

To multiply powers of the same base, add their exponents.

$$a^{16-8}$$

Add the exponents 16 and -8.

$$a^{8}$$

Differentiate w.r.t. a

$$8a^{7}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{16}}{a^{8}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 8 from 16 to get 8.

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

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

$$8a^{8-1}$$

Subtract 1 from 8.

$$8a^{7}$$