Sure! Let's rewrite the expression [tex]\(-2 \sqrt[3]{24} - 4 \sqrt[3]{81}\)[/tex] step-by-step and find its simplified numerical value.
1. Cube Root Calculation:
- First, find the cube root of 24.
[tex]\[
\sqrt[3]{24} \approx 2.8845
\][/tex]
- Next, find the cube root of 81.
[tex]\[
\sqrt[3]{81} \approx 4.3267
\][/tex]
2. Multiplication:
- Multiply the cube root of 24 by [tex]\(-2\)[/tex]:
[tex]\[
-2 \cdot \sqrt[3]{24} \approx -2 \cdot 2.8845 = -5.769
\][/tex]
- Multiply the cube root of 81 by [tex]\(-4\)[/tex]:
[tex]\[
-4 \cdot \sqrt[3]{81} \approx -4 \cdot 4.3267 = -17.307
\][/tex]
3. Addition:
- Add the two results from the above multiplications:
[tex]\[
-5.769 + (-17.307) = -23.076
\][/tex]
Thus, the entire expression simplifies to:
[tex]\[
-2 \sqrt[3]{24} - 4 \sqrt[3]{81} \approx -23.076
\][/tex]
So, the value of the expression [tex]\(-2 \sqrt[3]{24} - 4 \sqrt[3]{81}\)[/tex] is approximately [tex]\(-23.076\)[/tex].
