Solve 15ab^4/5ab^2=

$$\frac { 15 a b ^ { 4 } } { 5 a b ^ { 2 } } =$$

Evaluate

$$3b^{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{15^{1}a^{1}b^{4}}{5^{1}a^{1}b^{2}}$$

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

$$\frac{15^{1}}{5^{1}}a^{1-1}b^{4-2}$$

Subtract 1 from 1.

$$\frac{15^{1}}{5^{1}}a^{0}b^{4-2}$$

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

$$\frac{15^{1}}{5^{1}}b^{4-2}$$

Subtract 2 from 4.

$$\frac{15^{1}}{5^{1}}b^{2}$$

Divide 15 by 5.

$$3b^{2}$$

Differentiate w.r.t. b

$$6b$$

Steps Using Definition of a Derivative

Cancel out 5ab^{2} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}b}(3b^{2})$$

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

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

Multiply 2 times 3.

$$6b^{2-1}$$

Subtract 1 from 2.

$$6b^{1}$$

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

$$6b$$