Solve 8b^8b/2b^2

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

Evaluate

$$4b^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 8 and 1 to get 9.

$$\frac{8b^{9}}{2b^{2}}$$

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

$$4b^{7}$$

Differentiate w.r.t. b

$$28b^{6}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}b}(4bb^{6})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$6\times 4bb^{6-1}$$

Do the arithmetic.

$$24bb^{5}$$