Solve 40h/24h^2=

$$\frac { 40 h } { 24 h ^ { 2 } } =$$

Evaluate

$$\frac{5}{3h}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(40h^{1}\right)^{1}\times \frac{1}{24h^{2}}$$

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

$$40^{1}\left(h^{1}\right)^{1}\times \frac{1}{24}\times \frac{1}{h^{2}}$$

Use the Commutative Property of Multiplication.

$$40^{1}\times \frac{1}{24}\left(h^{1}\right)^{1}\times \frac{1}{h^{2}}$$

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

$$40^{1}\times \frac{1}{24}h^{1}h^{2\left(-1\right)}$$

Multiply 2 times -1.

$$40^{1}\times \frac{1}{24}h^{1}h^{-2}$$

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

$$40^{1}\times \frac{1}{24}h^{1-2}$$

Add the exponents 1 and -2.

$$40^{1}\times \frac{1}{24}\times \frac{1}{h}$$

Raise 40 to the power 1.

$$40\times \frac{1}{24}\times \frac{1}{h}$$

Multiply 40 times \frac{1}{24}.

$$\frac{5}{3}\times \frac{1}{h}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{40^{1}h^{1}}{24^{1}h^{2}}$$

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

$$\frac{40^{1}h^{1-2}}{24^{1}}$$

Subtract 2 from 1.

$$\frac{40^{1}\times \frac{1}{h}}{24^{1}}$$

Reduce the fraction \frac{40}{24} to lowest terms by extracting and canceling out 8.

$$\frac{5}{3}\times \frac{1}{h}$$

Differentiate w.r.t. h

$$-\frac{5}{3h^{2}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{40}{24}h^{1-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{5}{3}\times \frac{1}{h})$$

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}.

$$-\frac{5}{3}h^{-1-1}$$

Do the arithmetic.

$$-\frac{5}{3}h^{-2}$$