Question

Hi, could I have some help answering this question in the picture attached?simplify the question

Answer 1

`\text{-42}s^(-1)t^{(2)/(3)}`

Step-by-step explanation:

`\begin{gathered} (7s^{(7)/(4)}t^{(-5)/(3)})(-6s^{(-11)/(4)}t^{(7)/(3)}) \\ =\text{ }(7s^{(7)/(4)}* t^{(-5)/(3)})(-6s^{(-11)/(4)}* t^{(7)/(3)}) \end{gathered}`

Expand and collect like terms:

`\begin{gathered} =\text{ }7s^{(7)/(4)}* t^{(-5)/(3)}*-6s^{(-11)/(4)}* t^{(7)/(3)} \\ =\text{ }7* s^{(7)/(4)}*-6* s^{(-11)/(4)}* t^{(-5)/(3)}* t^{(7)/(3)} \\ =\text{ 7 }*-6\text{ }*\text{ }s^{(7)/(4)}* s^{(-11)/(4)}* t^{(-5)/(3)}* t^{(7)/(3)} \\ =\text{ -42}*\text{ }s^{(7)/(4)}* s^{(-11)/(4)}* t^{(-5)/(3)}* t^{(7)/(3)} \end{gathered}`

Bring the exponents having same base together:

`\begin{gathered} \text{The multiplication betwe}en\text{ same base becomes addition } \\ \text{when the exponents are brought together} \\ =-42\text{ }*\text{ }s^{(7)/(4)-(11)/(4)}* t^{(-5)/(3)+(7)/(3)} \\ =\text{ -42 }* s^{(7-11)/(4)}* t^{(-5+7)/(3)} \\ =\text{ -42 }* s^{(-4)/(4)}* t^{(2)/(3)} \end{gathered}`
`\begin{gathered} =\text{ -42 }* s^{(-4)/(4)}* t^{(2)/(3)} \\ =\text{ -42 }* s^(-1)* t^{(2)/(3)} \\ =\text{ -42}s^(-1)t^{(2)/(3)} \end{gathered}`