Solve 18s^3t^3/24s^2t=

$$\frac { 18 s ^ { 3 } t ^ { 3 } } { 24 s ^ { 2 } t } =$$

Evaluate

$$\frac{3st^{2}}{4}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{18^{1}s^{3}t^{3}}{24^{1}s^{2}t^{1}}$$

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

$$\frac{18^{1}}{24^{1}}s^{3-2}t^{3-1}$$

Subtract 2 from 3.

$$\frac{18^{1}}{24^{1}}s^{1}t^{3-1}$$

Subtract 1 from 3.

$$\frac{18^{1}}{24^{1}}st^{2}$$

Reduce the fraction \frac{18}{24} to lowest terms by extracting and canceling out 6.

$$\frac{3}{4}st^{2}$$

Differentiate w.r.t. s

$$\frac{3t^{2}}{4}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}s}(\frac{18t^{3}}{24t}s^{3-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}s}(\frac{3t^{2}}{4}s^{1})$$

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}.

$$\frac{3t^{2}}{4}s^{1-1}$$

Do the arithmetic.

$$\frac{3t^{2}}{4}s^{0}$$

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

$$\frac{3t^{2}}{4}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{3t^{2}}{4}$$