Solve 2b^3/-6b^9=

$$\frac { 2 b ^ { 3 } } { - 6 b ^ { 9 } } =$$

Evaluate

$$-\frac{1}{3b^{6}}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(2b^{3}\right)^{1}\times \frac{1}{-6b^{9}}$$

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

$$2^{1}\left(b^{3}\right)^{1}\times \frac{1}{-6}\times \frac{1}{b^{9}}$$

Use the Commutative Property of Multiplication.

$$2^{1}\times \frac{1}{-6}\left(b^{3}\right)^{1}\times \frac{1}{b^{9}}$$

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

$$2^{1}\times \frac{1}{-6}b^{3}b^{9\left(-1\right)}$$

Multiply 9 times -1.

$$2^{1}\times \frac{1}{-6}b^{3}b^{-9}$$

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

$$2^{1}\times \frac{1}{-6}b^{3-9}$$

Add the exponents 3 and -9.

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

Raise 2 to the power 1.

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

Raise -6 to the power -1.

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

Multiply 2 times -\frac{1}{6}.

$$-\frac{1}{3}b^{-6}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{2^{1}b^{3}}{\left(-6\right)^{1}b^{9}}$$

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

$$\frac{2^{1}b^{3-9}}{\left(-6\right)^{1}}$$

Subtract 9 from 3.

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

Reduce the fraction \frac{2}{-6} to lowest terms by extracting and canceling out 2.

$$-\frac{1}{3}b^{-6}$$

Differentiate w.r.t. b

$$\frac{2}{b^{7}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{2}{-6}b^{3-9})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}b}(-\frac{1}{3}b^{-6})$$

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}.

$$-6\left(-\frac{1}{3}\right)b^{-6-1}$$

Do the arithmetic.

$$2b^{-7}$$