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Answer :
Let's solve the problem step by step.
We need to find which one of the given options is equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
1. First, let's calculate [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
[tex]\[
\left(\frac{4}{5}\right)^6 = \frac{4^6}{5^6}
\][/tex]
2. Now let's compare this result with each option:
- Option A: [tex]\(6 \cdot \left(\frac{4}{5}\right)\)[/tex]
[tex]\[
6 \cdot \left(\frac{4}{5}\right) = 6 \cdot 0.8 = 4.8
\][/tex]
Clearly, 4.8 is not equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
- Option B: [tex]\(\frac{4^6}{5^5}\)[/tex]
[tex]\[
\frac{4^6}{5^5} = \frac{4096}{3125} \approx 1.31072
\][/tex]
This is also not equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
- Option C: [tex]\(\frac{24}{30}\)[/tex]
[tex]\[
\frac{24}{30} = 0.8
\][/tex]
This is not equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex] either.
- Option D: [tex]\(\frac{4^6}{5}\)[/tex]
[tex]\[
\frac{4^6}{5} = \frac{4096}{5} = 819.2
\][/tex]
Again, 819.2 is not equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
Reviewing the above comparisons, none of the given options exactly match with [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
Therefore, none of the provided options (A, B, C, or D) are equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
We need to find which one of the given options is equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
1. First, let's calculate [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
[tex]\[
\left(\frac{4}{5}\right)^6 = \frac{4^6}{5^6}
\][/tex]
2. Now let's compare this result with each option:
- Option A: [tex]\(6 \cdot \left(\frac{4}{5}\right)\)[/tex]
[tex]\[
6 \cdot \left(\frac{4}{5}\right) = 6 \cdot 0.8 = 4.8
\][/tex]
Clearly, 4.8 is not equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
- Option B: [tex]\(\frac{4^6}{5^5}\)[/tex]
[tex]\[
\frac{4^6}{5^5} = \frac{4096}{3125} \approx 1.31072
\][/tex]
This is also not equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
- Option C: [tex]\(\frac{24}{30}\)[/tex]
[tex]\[
\frac{24}{30} = 0.8
\][/tex]
This is not equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex] either.
- Option D: [tex]\(\frac{4^6}{5}\)[/tex]
[tex]\[
\frac{4^6}{5} = \frac{4096}{5} = 819.2
\][/tex]
Again, 819.2 is not equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
Reviewing the above comparisons, none of the given options exactly match with [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
Therefore, none of the provided options (A, B, C, or D) are equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
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