Solve (7s^frac{7{4}}t^frac{-5{3}})(-6s^frac{-11{4}}t^frac{7{3}})

$$( 7 s ^ { \frac { 7 } { 4 } } t ^ { \frac { - 5 } { 3 } } ) ( - 6 s ^ { \frac { - 11 } { 4 } } t ^ { \frac { 7 } { 3 } } )$$

Evaluate

$$-\frac{42t^{\frac{2}{3}}}{s}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$7^{1}s^{\frac{7}{4}}t^{-\frac{5}{3}}\left(-6\right)^{1}s^{-\frac{11}{4}}t^{\frac{7}{3}}$$

Use the Commutative Property of Multiplication.

$$7^{1}\left(-6\right)^{1}s^{\frac{7}{4}}s^{-\frac{11}{4}}t^{-\frac{5}{3}}t^{\frac{7}{3}}$$

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

$$7^{1}\left(-6\right)^{1}s^{\frac{7-11}{4}}t^{\frac{-5+7}{3}}$$

Add the exponents \frac{7}{4} and -\frac{11}{4}.

$$7^{1}\left(-6\right)^{1}\times \frac{1}{s}t^{\frac{-5+7}{3}}$$

Add the exponents -\frac{5}{3} and \frac{7}{3}.

$$7^{1}\left(-6\right)^{1}\times \frac{1}{s}t^{\frac{2}{3}}$$

Multiply 7 times -6.

$$-42\times \frac{1}{s}t^{\frac{2}{3}}$$

Differentiate w.r.t. t

$$-\frac{28}{\sqrt[3]{t}s}$$