Let's solve each part of the question step-by-step.
1. Calculate the fifth root of 32:
The fifth root of a number [tex]\(x\)[/tex] is the number [tex]\(y\)[/tex] such that [tex]\(y^5 = x\)[/tex]. In this case, we need to find [tex]\(y\)[/tex] such that:
[tex]\[ y^5 = 32 \][/tex]
We are looking for [tex]\( \sqrt[5]{32} \)[/tex].
We know that:
[tex]\[ 2^5 = 32 \][/tex]
Therefore, [tex]\( \sqrt[5]{32} = 2 \)[/tex].
So:
[tex]\[ \sqrt[5]{32} = 2 \][/tex]
2. Calculate the cube root of [tex]\(2^3\)[/tex]:
The cube root of a number [tex]\(x\)[/tex] is the number [tex]\(z\)[/tex] such that [tex]\(z^3 = x\)[/tex]. In this case, we need to find [tex]\(z\)[/tex] such that:
[tex]\[ z^3 = 2^3 \][/tex]
We know that:
[tex]\[ 2^3 = 8 \][/tex]
Therefore, we need to find [tex]\( \sqrt[3]{8} \)[/tex].
We know that:
[tex]\[ 2^3 = 8 \][/tex]
So:
[tex]\[ \sqrt[3]{2^3} = 2 \][/tex]
Thus:
[tex]\[ \sqrt[3]{2^3} = 2 \][/tex]
Therefore, the solutions to the given problems are:
[tex]\[ \sqrt[5]{32} = 2 \][/tex]
[tex]\[ \sqrt[3]{2^3} = 2 \][/tex]
These values are:
[tex]\[ \sqrt[5]{32} = 2.0 \][/tex]
[tex]\[ \sqrt[3]{2^3} = 2.0 \][/tex]
