Solve t^{3}u^2*t^-1u^0*tu^-7

$$t ^ { 3 } u ^ { 2 } \cdot t ^ { - 1 } u ^ { 0 } \cdot t u ^ { - 7 }$$

Evaluate

$$\frac{t^{3}}{u^{5}}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$t^{3}u^{2}\times \frac{1}{t}u^{0}u^{-7}t^{1}$$

Use the Commutative Property of Multiplication.

$$t^{3}u^{0}u^{2}u^{-7}\times \frac{1}{t}t^{1}$$

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

$$t^{3}u^{0}u^{2-7}t^{-1+1}$$

Add the exponents 2 and -7.

$$t^{3}u^{0}u^{-5}t^{-1+1}$$

Add the exponents -1 and 1.

$$t^{3}u^{0}\times \frac{1}{u^{5}}t^{0}$$

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

$$t^{3}u^{0}\times \frac{1}{u^{5}}$$

Raise u to the power 0.

$$t^{3}\times \frac{1}{u^{5}}$$

Differentiate w.r.t. t

$$\frac{3t^{2}}{u^{5}}$$