Solve b^15div(b^3)^4

$$b ^ { 15 } \div ( b ^ { 3 } ) ^ { 4 }$$

Evaluate

$$b^{3}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{b^{15}}{b^{12}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 12 from 15 to get 3.

$$b^{3}$$

Differentiate w.r.t. b

$$3b^{2}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{b^{15}}{b^{12}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 12 from 15 to get 3.

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

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

$$3b^{3-1}$$

Subtract 1 from 3.

$$3b^{2}$$