Solve 12m/15m^2=

$$\frac { 12 m } { 15 m ^ { 2 } } =$$

Evaluate

$$\frac{4}{5m}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(12m^{1}\right)^{1}\times \frac{1}{15m^{2}}$$

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

$$12^{1}\left(m^{1}\right)^{1}\times \frac{1}{15}\times \frac{1}{m^{2}}$$

Use the Commutative Property of Multiplication.

$$12^{1}\times \frac{1}{15}\left(m^{1}\right)^{1}\times \frac{1}{m^{2}}$$

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

$$12^{1}\times \frac{1}{15}m^{1}m^{2\left(-1\right)}$$

Multiply 2 times -1.

$$12^{1}\times \frac{1}{15}m^{1}m^{-2}$$

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

$$12^{1}\times \frac{1}{15}m^{1-2}$$

Add the exponents 1 and -2.

$$12^{1}\times \frac{1}{15}\times \frac{1}{m}$$

Raise 12 to the power 1.

$$12\times \frac{1}{15}\times \frac{1}{m}$$

Multiply 12 times \frac{1}{15}.

$$\frac{4}{5}\times \frac{1}{m}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{12^{1}m^{1}}{15^{1}m^{2}}$$

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

$$\frac{12^{1}m^{1-2}}{15^{1}}$$

Subtract 2 from 1.

$$\frac{12^{1}\times \frac{1}{m}}{15^{1}}$$

Reduce the fraction \frac{12}{15} to lowest terms by extracting and canceling out 3.

$$\frac{4}{5}\times \frac{1}{m}$$

Differentiate w.r.t. m

$$-\frac{4}{5m^{2}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{12}{15}m^{1-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{4}{5}\times \frac{1}{m})$$

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}.

$$-\frac{4}{5}m^{-1-1}$$

Do the arithmetic.

$$-\frac{4}{5}m^{-2}$$