Solve (b^2)^5/b^4

$$\frac { ( b ^ { 2 } ) ^ { 5 } } { b ^ { 4 } }$$

Evaluate

$$b^{6}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(b^{2}\right)^{5}\times \frac{1}{b^{4}}$$

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

$$b^{2\times 5}b^{4\left(-1\right)}$$

Multiply 2 times 5.

$$b^{10}b^{4\left(-1\right)}$$

Multiply 4 times -1.

$$b^{10}b^{-4}$$

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

$$b^{10-4}$$

Add the exponents 10 and -4.

$$b^{6}$$

Differentiate w.r.t. b

$$6b^{5}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{b^{10}}{b^{4}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 10 to get 6.

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

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

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

Subtract 1 from 6.

$$6b^{5}$$