Let's carefully go through each part of the question step by step.
1. Calculating [tex]\(\sqrt[3]{\frac{1}{64}}\)[/tex]:
To find the cube root of [tex]\(\frac{1}{64}\)[/tex], we need to determine a number that, when multiplied by itself three times, equals [tex]\(\frac{1}{64}\)[/tex].
[tex]\[
\sqrt[3]{\frac{1}{64}} = \left(\frac{1}{64}\right)^{\frac{1}{3}}
\][/tex]
The result of this calculation is:
[tex]\[
\sqrt[3]{\frac{1}{64}} = 0.25
\][/tex]
2. Calculating [tex]\(\sqrt[3]{64}\)[/tex]:
Next, we need to find the cube root of [tex]\(64\)[/tex]:
[tex]\[
\sqrt[3]{64} = 64^{\frac{1}{3}}
\][/tex]
The result of this calculation (which is very close to an integer due to numerical precision) is:
[tex]\[
\sqrt[3]{64} = 3.9999999999999996
\][/tex]
3. Calculating [tex]\(1 \times 1 \times 1\)[/tex]:
Here, we perform a simple multiplication:
[tex]\[
1 \times 1 \times 1 = 1
\][/tex]
4. Calculating [tex]\(4 \times 4 \times 4\)[/tex]:
Finally, we multiply [tex]\(4\)[/tex] by itself three times:
[tex]\[
4 \times 4 \times 4 = 64
\][/tex]
To summarize, the detailed step-by-step solutions for each part are:
- [tex]\(\sqrt[3]{\frac{1}{64}} = 0.25\)[/tex]
- [tex]\(\sqrt[3]{64} = 3.9999999999999996\)[/tex]
- [tex]\(1 \times 1 \times 1 = 1\)[/tex]
- [tex]\(4 \times 4 \times 4 = 64\)[/tex]
Thus, the resulting values are:
[tex]\[
(0.25, 3.9999999999999996, 1, 64)
\][/tex]
