Answer :
To evaluate [tex]\(125^{\frac{2}{3}}\)[/tex], we can break down the expression step-by-step using the properties of exponents. The expression [tex]\(125^{\frac{2}{3}}\)[/tex] essentially means we first take the cube root of 125, and then square the result.
Here's the process:
1. Find the cube root of 125:
- The cube root of a number [tex]\(x\)[/tex] is the number that, when multiplied by itself three times, equals [tex]\(x\)[/tex].
- In this case, you need to find the cube root of 125, which is [tex]\(\sqrt[3]{125}\)[/tex].
- Since [tex]\(5 \times 5 \times 5 = 125\)[/tex], the cube root of 125 is 5.
2. Square the result:
- After finding that the cube root of 125 is 5, we then square this result.
- Squaring means multiplying the number by itself: [tex]\(5 \times 5 = 25\)[/tex].
Therefore, evaluating [tex]\(125^{\frac{2}{3}}\)[/tex] gives us 25.
The correct answer is (B) 25.
Here's the process:
1. Find the cube root of 125:
- The cube root of a number [tex]\(x\)[/tex] is the number that, when multiplied by itself three times, equals [tex]\(x\)[/tex].
- In this case, you need to find the cube root of 125, which is [tex]\(\sqrt[3]{125}\)[/tex].
- Since [tex]\(5 \times 5 \times 5 = 125\)[/tex], the cube root of 125 is 5.
2. Square the result:
- After finding that the cube root of 125 is 5, we then square this result.
- Squaring means multiplying the number by itself: [tex]\(5 \times 5 = 25\)[/tex].
Therefore, evaluating [tex]\(125^{\frac{2}{3}}\)[/tex] gives us 25.
The correct answer is (B) 25.
