Greene Hills
03/19/2023 · Junior High School
Evaluate the expression. \( \begin{array}{l}\text { 5. }\left(-\frac{4}{9}\right)^{3} \\ \text { 6. }\left(-\frac{2}{3}\right)^{5} \\ \text { 7. }-(2.5)^{3} \\ \text { 8. }(-3.4)^{2}\end{array} \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
Let's evaluate each expression step by step.
**5.** \( \left(-\frac{4}{9}\right)^{3} \)
To calculate this, we raise \(-\frac{4}{9}\) to the power of 3:
\[
\left(-\frac{4}{9}\right)^{3} = -\frac{4^3}{9^3} = -\frac{64}{729}
\]
**6.** \( \left(-\frac{2}{3}\right)^{5} \)
Now we raise \(-\frac{2}{3}\) to the power of 5:
\[
\left(-\frac{2}{3}\right)^{5} = -\frac{2^5}{3^5} = -\frac{32}{243}
\]
**7.** \( -(2.5)^{3} \)
First, we calculate \( (2.5)^{3} \):
\[
(2.5)^{3} = 2.5 \times 2.5 \times 2.5 = 6.25 \times 2.5 = 15.625
\]
Now, we apply the negative sign:
\[
-(2.5)^{3} = -15.625
\]
**8.** \( (-3.4)^{2} \)
Next, we calculate \( (-3.4)^{2} \):
\[
(-3.4)^{2} = (-3.4) \times (-3.4) = 11.56
\]
Now, summarizing all the results:
1. \( \left(-\frac{4}{9}\right)^{3} = -\frac{64}{729} \)
2. \( \left(-\frac{2}{3}\right)^{5} = -\frac{32}{243} \)
3. \( -(2.5)^{3} = -15.625 \)
4. \( (-3.4)^{2} = 11.56 \)
Thus, the final evaluated expressions are:
\[
\begin{array}{l}
5. \quad -\frac{64}{729} \\
6. \quad -\frac{32}{243} \\
7. \quad -15.625 \\
8. \quad 11.56
\end{array}
\]
Quick Answer
\[
\begin{array}{l}
5. \quad -\frac{64}{729} \\
6. \quad -\frac{32}{243} \\
7. \quad -15.625 \\
8. \quad 11.56
\end{array}
\]
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