Answer :
To solve the problem, we want to find out which option is equal to the expression [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
Let's break down each option to see which one matches [tex]\(\left(\frac{4}{5}\right)^6\)[/tex]:
1. Option A: [tex]\(\frac{4^6}{5}\)[/tex]
- Calculate [tex]\(4^6\)[/tex]: [tex]\(4^6 = 4096\)[/tex].
- Evaluate [tex]\(\frac{4^6}{5}\)[/tex]: This results in [tex]\(\frac{4096}{5} = 819.2\)[/tex].
2. Option B: [tex]\(6 \cdot \left(\frac{4}{5}\right)\)[/tex]
- Here we perform [tex]\(6 \times \frac{4}{5}\)[/tex].
- Calculate [tex]\(6 \times 0.8 = 4.8\)[/tex].
3. Option C: [tex]\(\frac{24}{30}\)[/tex]
- Simplify [tex]\(\frac{24}{30}\)[/tex]: It simplifies to [tex]\(\frac{4}{5} = 0.8\)[/tex].
4. Option D: [tex]\(\frac{4^6}{5^6}\)[/tex]
- Calculate [tex]\(4^6 = 4096\)[/tex] and [tex]\(5^6 = 15625\)[/tex].
- Evaluate [tex]\(\frac{4096}{15625}\)[/tex], which gives approximately [tex]\(0.262144\)[/tex].
Now, compare each option with [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
- The expression [tex]\(\left(\frac{4}{5}\right)^6\)[/tex] calculates to approximately [tex]\(0.262144\)[/tex].
By comparing these values, we can see that:
- Option A: [tex]\(819.2\)[/tex] does not match.
- Option B: [tex]\(4.8\)[/tex] does not match.
- Option C: [tex]\(0.8\)[/tex] does not match.
- Option D: [tex]\(0.262144\)[/tex] matches.
Thus, the correct answer is Option D: [tex]\(\frac{4^6}{5^6}\)[/tex], as it correctly equals [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
Let's break down each option to see which one matches [tex]\(\left(\frac{4}{5}\right)^6\)[/tex]:
1. Option A: [tex]\(\frac{4^6}{5}\)[/tex]
- Calculate [tex]\(4^6\)[/tex]: [tex]\(4^6 = 4096\)[/tex].
- Evaluate [tex]\(\frac{4^6}{5}\)[/tex]: This results in [tex]\(\frac{4096}{5} = 819.2\)[/tex].
2. Option B: [tex]\(6 \cdot \left(\frac{4}{5}\right)\)[/tex]
- Here we perform [tex]\(6 \times \frac{4}{5}\)[/tex].
- Calculate [tex]\(6 \times 0.8 = 4.8\)[/tex].
3. Option C: [tex]\(\frac{24}{30}\)[/tex]
- Simplify [tex]\(\frac{24}{30}\)[/tex]: It simplifies to [tex]\(\frac{4}{5} = 0.8\)[/tex].
4. Option D: [tex]\(\frac{4^6}{5^6}\)[/tex]
- Calculate [tex]\(4^6 = 4096\)[/tex] and [tex]\(5^6 = 15625\)[/tex].
- Evaluate [tex]\(\frac{4096}{15625}\)[/tex], which gives approximately [tex]\(0.262144\)[/tex].
Now, compare each option with [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
- The expression [tex]\(\left(\frac{4}{5}\right)^6\)[/tex] calculates to approximately [tex]\(0.262144\)[/tex].
By comparing these values, we can see that:
- Option A: [tex]\(819.2\)[/tex] does not match.
- Option B: [tex]\(4.8\)[/tex] does not match.
- Option C: [tex]\(0.8\)[/tex] does not match.
- Option D: [tex]\(0.262144\)[/tex] matches.
Thus, the correct answer is Option D: [tex]\(\frac{4^6}{5^6}\)[/tex], as it correctly equals [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
