Solve (10b^6)div(5b^2)

$$( 10 b ^ { 6 } ) \div ( 5 b ^ { 2 } )$$

Evaluate

$$2b^{4}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(10b^{6}\right)^{1}\times \frac{1}{5b^{2}}$$

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

$$10^{1}\left(b^{6}\right)^{1}\times \frac{1}{5}\times \frac{1}{b^{2}}$$

Use the Commutative Property of Multiplication.

$$10^{1}\times \frac{1}{5}\left(b^{6}\right)^{1}\times \frac{1}{b^{2}}$$

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

$$10^{1}\times \frac{1}{5}b^{6}b^{2\left(-1\right)}$$

Multiply 2 times -1.

$$10^{1}\times \frac{1}{5}b^{6}b^{-2}$$

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

$$10^{1}\times \frac{1}{5}b^{6-2}$$

Add the exponents 6 and -2.

$$10^{1}\times \frac{1}{5}b^{4}$$

Raise 10 to the power 1.

$$10\times \frac{1}{5}b^{4}$$

Multiply 10 times \frac{1}{5}.

$$2b^{4}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{10^{1}b^{6}}{5^{1}b^{2}}$$

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

$$\frac{10^{1}b^{6-2}}{5^{1}}$$

Subtract 2 from 6.

$$\frac{10^{1}b^{4}}{5^{1}}$$

Divide 10 by 5.

$$2b^{4}$$

Differentiate w.r.t. b

$$8b^{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{10}{5}b^{6-2})$$

Do the arithmetic.

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

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}.

$$4\times 2b^{4-1}$$

Do the arithmetic.

$$8b^{3}$$