Solve st^-1*s^3t*s^3t^-1

$$s t ^ { - 1 } \cdot s ^ { 3 } t \cdot s ^ { 3 } t ^ { - 1 }$$

Evaluate

$$\frac{s^{7}}{t}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$s^{1}\times \frac{1}{t}s^{3}t^{1}\times \frac{1}{t}s^{3}$$

Use the Commutative Property of Multiplication.

$$s^{1}t^{1}\times \frac{1}{t}\times \frac{1}{t}s^{3}s^{3}$$

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

$$s^{1}t^{1}t^{-1-1}s^{3+3}$$

Add the exponents -1 and -1.

$$s^{1}t^{1}t^{-2}s^{3+3}$$

Add the exponents 3 and 3.

$$s^{1}t^{1}\times \frac{1}{t^{2}}s^{6}$$

Multiply s times t.

$$st\times \frac{1}{t^{2}}s^{6}$$

Differentiate w.r.t. s

$$\frac{7s^{6}}{t}$$