Solve 6m^9/3m^2

$$\frac { 6 m ^ { 9 } } { 3 m ^ { 2 } }$$

Evaluate

$$2m^{7}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply 2 times -1.

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

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

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

Add the exponents 9 and -2.

$$6^{1}\times \frac{1}{3}m^{7}$$

Raise 6 to the power 1.

$$6\times \frac{1}{3}m^{7}$$

Multiply 6 times \frac{1}{3}.

$$2m^{7}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{6^{1}m^{9}}{3^{1}m^{2}}$$

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

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

Subtract 2 from 9.

$$\frac{6^{1}m^{7}}{3^{1}}$$

Divide 6 by 3.

$$2m^{7}$$

Differentiate w.r.t. m

$$14m^{6}$$

Solution Steps

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

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}m}(2m^{7})$$

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}.

$$7\times 2m^{7-1}$$

Do the arithmetic.

$$14m^{6}$$