Questions: Exponents and signed fractions 0 / 3 Evaluate. Write your answer 4^2 / -5 = - (5 / 2)^3 =

$Exponents and signed fractions 0 / 3 Evaluate. Write your answer 4^2 / -5 = - (5 / 2)^3 =$

Transcript text: Exponents and signed fractions $\square$ $0 / 3$ Evaluate. Write your ansv \[ \begin{array}{r} \frac{4^{2}}{-5}=\square \\ -\left(\frac{5}{2}\right)^{3}=\square \end{array} \]

Solution

Solution Steps

To solve the given problems, we need to evaluate the expressions involving exponents and signed fractions.

For the first expression, $\frac{4^2}{-5}$, we need to calculate $4^2$ and then divide the result by $-5$.
For the second expression, $-\left(\frac{5}{2}\right)^3$, we need to calculate $\left(\frac{5}{2}\right)^3$ and then apply the negative sign to the result.

Step 1: Evaluate $ \frac{4^2}{-5} $

First, we calculate $ 4^2 $: \[ 4^2 = 16 \] Next, we divide by $-5$: \[ \frac{16}{-5} = -3.2 \]

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

First, we calculate $ \left(\frac{5}{2}\right)^3 $: \[ \left(\frac{5}{2}\right)^3 = \frac{5^3}{2^3} = \frac{125}{8} \] Now, we apply the negative sign: \[ -\left(\frac{5}{2}\right)^3 = -\frac{125}{8} = -15.625 \]

Final Answer

The results of the evaluations are: \[ \frac{4^2}{-5} = -3.2 \quad \text{and} \quad -\left(\frac{5}{2}\right)^3 = -15.625 \] Thus, the final answers are: \[ \boxed{-3.2} \quad \text{and} \quad \boxed{-15.625} \]

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!