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

Explanation

let's remember some properties of the exponents

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

hence

Step 1

$\begin{gathered} 3.2^{1.5} \\ 3.2^{1.5}=3.2^1+3.2^{0.5} \\ 3.2^{1.5}=3.2+\sqrt{3.2} \\ 3.2^{1.5}=5.72 \end{gathered}$

Step 2

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

so, the answer is

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

I hope this helps you