Solve a^4diva^3*a^7=

$$a ^ { 4 } \div a ^ { 3 } \times a ^ { 7 } =$$

Evaluate

$$a^{8}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 4 to get 1.

$$a^{1}a^{7}$$

To multiply powers of the same base, add their exponents. Add 1 and 7 to get 8.

$$a^{8}$$

Differentiate w.r.t. a

$$8a^{7}$$

Steps Using Definition of a Derivative

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 4 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{1}a^{7})$$

To multiply powers of the same base, add their exponents. Add 1 and 7 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.

$$8a^{7}$$