Solve a^7a^0a^-3a^4=

$$a ^ { 7 } a ^ { 0 } a ^ { - 3 } a ^ { 4 } =$$

Evaluate

$$a^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and 0 to get 7.

$$a^{7}a^{-3}a^{4}$$

To multiply powers of the same base, add their exponents. Add 7 and -3 to get 4.

$$a^{4}a^{4}$$

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

$$a^{8}$$

Differentiate w.r.t. a

$$8a^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 7 and 0 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{7}a^{-3}a^{4})$$

To multiply powers of the same base, add their exponents. Add 7 and -3 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{4}a^{4})$$

To multiply powers of the same base, add their exponents. Add 4 and 4 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.

$$8a^{7}$$