Question
\( 2.1 .4 \sqrt { 25 } + \sqrt[ 3 ] { - 125 } + ( - 2 ) ^ { 2 } ( - 2 ) ^ { 3 } \)
Ask by Page Brewer. in South Africa
Mar 16,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The final answer is \(-23\).
Solution
We start with the expression
\[
2 \times 1.4 \times \sqrt{25} + \sqrt[3]{-125} + (-2)^2 \times (-2)^3.
\]
**Step 1. Evaluate \(\sqrt{25}\):**
\[
\sqrt{25} = 5.
\]
The first term becomes
\[
2 \times 1.4 \times 5.
\]
**Step 2. Multiply the numbers in the first term:**
\[
2 \times 1.4 = 2.8,
\]
\[
2.8 \times 5 = 14.
\]
So, the first term is \(14\).
**Step 3. Evaluate the cube root \(\sqrt[3]{-125}\):**
Since
\[
(-5)^3 = -125,
\]
it follows that
\[
\sqrt[3]{-125} = -5.
\]
**Step 4. Evaluate \((-2)^2 \times (-2)^3\):**
Compute each part separately:
\[
(-2)^2 = 4,
\]
\[
(-2)^3 = -8.
\]
Now multiply them:
\[
4 \times (-8) = -32.
\]
**Step 5. Sum all the evaluated parts:**
\[
14 + (-5) + (-32) = 14 - 5 - 32.
\]
First, \(14 - 5 = 9\), then
\[
9 - 32 = -23.
\]
The final answer is
\[
-23.
\]
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Bonus Knowledge
Let's break it down step by step! First, we calculate \( \sqrt{25} \) which equals 5, so \( 2.1 \times 4 \times 5 \) gives us \( 42 \). Next, \( \sqrt[3]{-125} \) is \(-5\) because the cube root of \(-125\) is \(-5\). For \( (-2)^2 \times (-2)^3 \), we find \( (-2)^2 = 4 \) and \( (-2)^3 = -8 \), leading to \( 4 \times -8 = -32 \). Adding these values together: \( 42 - 5 - 32 \) results in \( 5 \). So the final result is \( 5 \).