Solve 56s^2t^3/4s^2t=

$$\frac { 56 s ^ { 2 } t ^ { 3 } } { 4 s ^ { 2 } t } =$$

Evaluate

$$14t^{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{56^{1}s^{2}t^{3}}{4^{1}s^{2}t^{1}}$$

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

$$\frac{56^{1}}{4^{1}}s^{2-2}t^{3-1}$$

Subtract 2 from 2.

$$\frac{56^{1}}{4^{1}}s^{0}t^{3-1}$$

For any number a except 0, a^{0}=1.

$$\frac{56^{1}}{4^{1}}t^{3-1}$$

Subtract 1 from 3.

$$\frac{56^{1}}{4^{1}}t^{2}$$

Divide 56 by 4.

$$14t^{2}$$

Differentiate w.r.t. t

$$28t$$

Steps Using Definition of a Derivative

Cancel out 4ts^{2} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}t}(14t^{2})$$

The derivative of ax^{n} is nax^{n-1}.

$$2\times 14t^{2-1}$$

Multiply 2 times 14.

$$28t^{2-1}$$

Subtract 1 from 2.

$$28t^{1}$$

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

$$28t$$