Question

Evaluate each expression.Round your answers to the nearest thousandth. Do not do any intermediate computations (THIS IS ONE QUESTION I DO AN ONLINE MATH PROGRAM WHERE THIS IS CONSIDERED ONE QUESTION)

Answer 1

Step-by-step explanation

let's remember some properties of the exponents

`\begin{gathered} ((a)/(b))^n=(a^n)/(b^n) \\ ((a)/(b))^(-n)=(n^n)/(a^n) \\ a^m*a^n=a^(m+n) \end{gathered}`

hence

Step 1

`\begin{gathered} 3.2^(1.5) \\ 3.2^(1.5)=3.2^1+3.2^(0.5) \\ 3.2^(1.5)=3.2+√(3.2) \\ 3.2^(1.5)=5.72 \end{gathered}`

Step 2

`\begin{gathered} ((3)/(5))^(-0.85) \\ ((3)/(5))^(-0.85)=(5^(0.85))/(3^(0.85))=1.54373 \\ ((3)/(5))^(-0.85)=1.544 \end{gathered}`

so, the answer is

`\begin{gathered} 3.2^(1.5)=5.72 \\ ((3)/(5))^(-0.85)=1.544 \end{gathered}`

I hope this helps you