Solve 10h^8b^3/60h^8b

$$\frac { 10 h ^ { 8 } b ^ { 3 } } { 60 h ^ { 8 } b }$$

Evaluate

$$\frac{b^{2}}{6}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{10^{1}h^{8}b^{3}}{60^{1}h^{8}b^{1}}$$

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

$$\frac{10^{1}}{60^{1}}h^{8-8}b^{3-1}$$

Subtract 8 from 8.

$$\frac{10^{1}}{60^{1}}h^{0}b^{3-1}$$

For any number a except 0, a^{0}=1.

$$\frac{10^{1}}{60^{1}}b^{3-1}$$

Subtract 1 from 3.

$$\frac{10^{1}}{60^{1}}b^{2}$$

Reduce the fraction \frac{10}{60} to lowest terms by extracting and canceling out 10.

$$\frac{1}{6}b^{2}$$

Differentiate w.r.t. b

$$\frac{b}{3}$$

Steps Using Definition of a Derivative

Cancel out 10bh^{8} in both numerator and denominator.

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

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

$$2\times \frac{1}{6}b^{2-1}$$

Multiply 2 times \frac{1}{6}.

$$\frac{1}{3}b^{2-1}$$

Subtract 1 from 2.

$$\frac{1}{3}b^{1}$$

For any term t, t^{1}=t.

$$\frac{1}{3}b$$