Questions: -5/3^2= (-5/3)^3=

Transcript text: $\begin{array}{r}\frac{-5}{3^{2}}= \\ \left(-\frac{5}{3}\right)^{3}=\end{array}$

Solution

Solution Steps

To solve the given expressions, we need to evaluate each one separately. The first expression is a simple division and exponentiation, while the second expression involves raising a fraction to a power. We will use Python to perform these calculations.

Step 1: Evaluate $\frac{-5}{3^2}$

To solve the expression $\frac{-5}{3^2}$, we first calculate $3^2$, which is $9$. Then, we divide $-5$ by $9$:

\[ \frac{-5}{9} = -0.5556 \]

Step 2: Evaluate $\left(-\frac{5}{3}\right)^3$

For the expression $\left(-\frac{5}{3}\right)^3$, we first calculate $-\frac{5}{3}$, which is approximately $-1.6667$. Then, we raise this value to the power of $3$:

\[ \left(-\frac{5}{3}\right)^3 = -4.630 \]