Answer :

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]