Answer :
To determine which option is equal to the fraction [tex]\(\left(\frac{4}{5}\right)^6\)[/tex], let's evaluate each choice and compare them to the expression:
1. Evaluate the expression [tex]\(\left(\frac{4}{5}\right)^6 \)[/tex]:
- Compute [tex]\((\frac{4}{5})^6\)[/tex].
- This gives us approximately 0.262144.
2. Evaluate each option:
- Option A: [tex]\(6 \cdot \left(\frac{4}{5}\right)\)[/tex]
- Calculate: [tex]\(6 \times 0.8 = 4.8\)[/tex]
- This is clearly not equal to 0.262144.
- Option B: [tex]\(\frac{4^6}{5^6}\)[/tex]
- Let's compute: [tex]\(\frac{4096}{15625}\)[/tex]
- This equals approximately 0.262144, which matches the expression [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
- Option C: [tex]\(\frac{4^6}{5}\)[/tex]
- Calculate: [tex]\(\frac{4096}{5} = 819.2\)[/tex]
- This is not equal to 0.262144.
- Option D: [tex]\(\frac{24}{30}\)[/tex]
- Simplify: [tex]\(\frac{24}{30} = 0.8\)[/tex]
- This is not equal to 0.262144.
3. Comparison:
From the calculations, option B gives us the same value as [tex]\(\left(\frac{4}{5}\right)^6\)[/tex], which is approximately 0.262144.
Therefore, the correct choice is B. [tex]\(\frac{4^6}{5^6}\)[/tex].
1. Evaluate the expression [tex]\(\left(\frac{4}{5}\right)^6 \)[/tex]:
- Compute [tex]\((\frac{4}{5})^6\)[/tex].
- This gives us approximately 0.262144.
2. Evaluate each option:
- Option A: [tex]\(6 \cdot \left(\frac{4}{5}\right)\)[/tex]
- Calculate: [tex]\(6 \times 0.8 = 4.8\)[/tex]
- This is clearly not equal to 0.262144.
- Option B: [tex]\(\frac{4^6}{5^6}\)[/tex]
- Let's compute: [tex]\(\frac{4096}{15625}\)[/tex]
- This equals approximately 0.262144, which matches the expression [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
- Option C: [tex]\(\frac{4^6}{5}\)[/tex]
- Calculate: [tex]\(\frac{4096}{5} = 819.2\)[/tex]
- This is not equal to 0.262144.
- Option D: [tex]\(\frac{24}{30}\)[/tex]
- Simplify: [tex]\(\frac{24}{30} = 0.8\)[/tex]
- This is not equal to 0.262144.
3. Comparison:
From the calculations, option B gives us the same value as [tex]\(\left(\frac{4}{5}\right)^6\)[/tex], which is approximately 0.262144.
Therefore, the correct choice is B. [tex]\(\frac{4^6}{5^6}\)[/tex].
