Solve 8b^12/4b^2

$$\frac { 8 b ^ { 12 } } { 4 b ^ { 2 } }$$

Evaluate

$$2b^{10}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(8b^{12}\right)^{1}\times \frac{1}{4b^{2}}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$8^{1}\left(b^{12}\right)^{1}\times \frac{1}{4}\times \frac{1}{b^{2}}$$

Use the Commutative Property of Multiplication.

$$8^{1}\times \frac{1}{4}\left(b^{12}\right)^{1}\times \frac{1}{b^{2}}$$

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

$$8^{1}\times \frac{1}{4}b^{12}b^{2\left(-1\right)}$$

Multiply 2 times -1.

$$8^{1}\times \frac{1}{4}b^{12}b^{-2}$$

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

$$8^{1}\times \frac{1}{4}b^{12-2}$$

Add the exponents 12 and -2.

$$8^{1}\times \frac{1}{4}b^{10}$$

Raise 8 to the power 1.

$$8\times \frac{1}{4}b^{10}$$

Multiply 8 times \frac{1}{4}.

$$2b^{10}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{8^{1}b^{12}}{4^{1}b^{2}}$$

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

$$\frac{8^{1}b^{12-2}}{4^{1}}$$

Subtract 2 from 12.

$$\frac{8^{1}b^{10}}{4^{1}}$$

Divide 8 by 4.

$$2b^{10}$$

Differentiate w.r.t. b

$$20b^{9}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{8}{4}b^{12-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}b}(2b^{10})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$10\times 2b^{10-1}$$

Do the arithmetic.

$$20b^{9}$$