Solve 15b^9divb^2

$$15 b ^ { 9 } \div b ^ { 2 }$$

Evaluate

$$15b^{7}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(15b^{9}\right)^{1}\times \frac{1}{b^{2}}$$

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

$$15^{1}\left(b^{9}\right)^{1}\times \frac{1}{1}\times \frac{1}{b^{2}}$$

Use the Commutative Property of Multiplication.

$$15^{1}\times \frac{1}{1}\left(b^{9}\right)^{1}\times \frac{1}{b^{2}}$$

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

$$15^{1}\times \frac{1}{1}b^{9}b^{2\left(-1\right)}$$

Multiply 2 times -1.

$$15^{1}\times \frac{1}{1}b^{9}b^{-2}$$

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

$$15^{1}\times \frac{1}{1}b^{9-2}$$

Add the exponents 9 and -2.

$$15^{1}\times \frac{1}{1}b^{7}$$

Raise 15 to the power 1.

$$15\times \frac{1}{1}b^{7}$$

Differentiate w.r.t. b

$$105b^{6}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{15}{1}b^{9-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}b}(15b^{7})$$

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}.

$$7\times 15b^{7-1}$$

Do the arithmetic.

$$105b^{6}$$