Solve a^5b^6diva^5b^2

$$a ^ { 5 } b ^ { 6 } \div a ^ { 5 } b ^ { 2 }$$

Evaluate

$$b^{8}$$

Solution Steps

Cancel out a^{5} in both numerator and denominator.

$$b^{6}b^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$b^{8}$$

Differentiate w.r.t. b

$$8b^{7}$$

Steps Using Definition of a Derivative

Cancel out a^{5} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b^{6}b^{2})$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

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

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

$$8b^{8-1}$$

Subtract 1 from 8.

$$8b^{7}$$