Solve 6m^3div(-3m^2)=

$$6 m ^ { 3 } \div ( - 3 m ^ { 2 } ) =$$

Evaluate

$$-2m$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply 2 times -1.

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

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

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

Add the exponents 3 and -2.

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

Raise 6 to the power 1.

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

Raise -3 to the power -1.

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

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

$$-2m^{1}$$

For any term t, t^{1}=t.

$$-2m$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Subtract 2 from 3.

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

Divide 6 by -3.

$$-2m^{1}$$

For any term t, t^{1}=t.

$$-2m$$

Differentiate w.r.t. m

$$-2$$

Solution Steps

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

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}m}(-2m^{1})$$

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}.

$$-2m^{1-1}$$

Do the arithmetic.

$$-2m^{0}$$

For any term t except 0, t^{0}=1.

$$-2$$