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Answer :
To find which of the given options is equal to the fraction [tex]\(\left(\frac{4}{5}\right)^6\)[/tex], let's evaluate each option.
1. Evaluate the original fraction:
[tex]\[
\left(\frac{4}{5}\right)^6 = 0.262144
\][/tex]
2. Check each option:
- Option A: [tex]\(\frac{4^6}{5^6}\)[/tex]
[tex]\[
4^6 = 4096 \quad \text{and} \quad 5^6 = 15625
\][/tex]
Therefore,
[tex]\[
\frac{4^6}{5^6} = \frac{4096}{15625} = 0.262144
\][/tex]
This matches the original expression, so Option A is a candidate.
- Option B: [tex]\(6 \cdot\left(\frac{4}{5}\right)\)[/tex]
[tex]\[
6 \times \frac{4}{5} = 6 \times 0.8 = 4.8
\][/tex]
This does not match the original expression.
- Option C: [tex]\(\frac{24}{30}\)[/tex]
[tex]\[
\frac{24}{30} = \frac{4}{5} = 0.8
\][/tex]
This does not match the original expression.
- Option D: [tex]\(\frac{4^6}{5}\)[/tex]
[tex]\[
\frac{4^6}{5} = \frac{4096}{5} = 819.2
\][/tex]
This does not match the original expression.
Based on the evaluations above, the option that matches the original fraction [tex]\(\left(\frac{4}{5}\right)^6\)[/tex] is Option A: [tex]\(\frac{4^6}{5^6}\)[/tex].
1. Evaluate the original fraction:
[tex]\[
\left(\frac{4}{5}\right)^6 = 0.262144
\][/tex]
2. Check each option:
- Option A: [tex]\(\frac{4^6}{5^6}\)[/tex]
[tex]\[
4^6 = 4096 \quad \text{and} \quad 5^6 = 15625
\][/tex]
Therefore,
[tex]\[
\frac{4^6}{5^6} = \frac{4096}{15625} = 0.262144
\][/tex]
This matches the original expression, so Option A is a candidate.
- Option B: [tex]\(6 \cdot\left(\frac{4}{5}\right)\)[/tex]
[tex]\[
6 \times \frac{4}{5} = 6 \times 0.8 = 4.8
\][/tex]
This does not match the original expression.
- Option C: [tex]\(\frac{24}{30}\)[/tex]
[tex]\[
\frac{24}{30} = \frac{4}{5} = 0.8
\][/tex]
This does not match the original expression.
- Option D: [tex]\(\frac{4^6}{5}\)[/tex]
[tex]\[
\frac{4^6}{5} = \frac{4096}{5} = 819.2
\][/tex]
This does not match the original expression.
Based on the evaluations above, the option that matches the original fraction [tex]\(\left(\frac{4}{5}\right)^6\)[/tex] is Option A: [tex]\(\frac{4^6}{5^6}\)[/tex].
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