Solve (b^3)^2/b^2

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

Evaluate

$$b^{4}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(b^{3}\right)^{2}\times \frac{1}{b^{2}}$$

To raise a power to another power, multiply the exponents.

$$b^{3\times 2}b^{2\left(-1\right)}$$

Multiply 3 times 2.

$$b^{6}b^{2\left(-1\right)}$$

Multiply 2 times -1.

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

To multiply powers of the same base, add their exponents.

$$b^{6-2}$$

Add the exponents 6 and -2.

$$b^{4}$$

Differentiate w.r.t. b

$$4b^{3}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 6 to get 4.

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

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

$$4b^{4-1}$$

Subtract 1 from 4.

$$4b^{3}$$