Sure, let's break down the solution step-by-step.
We need to find the value of
[tex]\[ \sqrt[5]{(32)^2} \cdot \sqrt[3]{125^2} \][/tex]
1. First, evaluate [tex]\( \sqrt[5]{(32)^2} \)[/tex]:
- Calculate [tex]\( 32^2 \)[/tex]:
[tex]\[ 32^2 = 1024 \][/tex]
- Now find the fifth root of 1024:
[tex]\[ \sqrt[5]{1024} = 4 \][/tex]
So,
[tex]\[ \sqrt[5]{(32)^2} = 4 \][/tex]
2. Next, evaluate [tex]\( \sqrt[3]{125^2} \)[/tex]:
- Calculate [tex]\( 125^2 \)[/tex]:
[tex]\[ 125^2 = 15625 \][/tex]
- Now find the cube root of 15625:
[tex]\[ \sqrt[3]{15625} = 25 \][/tex]
So,
[tex]\[ \sqrt[3]{125^2} = 25 \][/tex]
3. Multiply the two results together:
- Multiply [tex]\( 4 \)[/tex] by [tex]\( 25 \)[/tex]:
[tex]\[ 4 \cdot 25 = 100 \][/tex]
Therefore,
[tex]\[ \sqrt[5]{(32)^2} \cdot \sqrt[3]{125^2} = 100 \][/tex]
