Solve 16s^2t/64st^2

$$\frac { 16 s ^ { 2 } t } { 64 s t ^ { 2 } }$$

Evaluate

$$\frac{s}{4t}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{16^{1}s^{2}t^{1}}{64^{1}s^{1}t^{2}}$$

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

$$\frac{16^{1}}{64^{1}}s^{2-1}t^{1-2}$$

Subtract 1 from 2.

$$\frac{16^{1}}{64^{1}}s^{1}t^{1-2}$$

Subtract 2 from 1.

$$\frac{16^{1}}{64^{1}}s\times \frac{1}{t}$$

Reduce the fraction \frac{16}{64} to lowest terms by extracting and canceling out 16.

$$\frac{1}{4}s\times \frac{1}{t}$$

Differentiate w.r.t. t

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