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Answer :
To find which expression is equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex], we need to analyze each option.
### Given Expression:
[tex]\[
\left(\frac{4}{5}\right)^6 = \frac{4^6}{5^6}
\][/tex]
Let's evaluate each option to see which matches this.
### Option A: [tex]\(6 \cdot \left(\frac{4}{5}\right)\)[/tex]
This expression simplifies as follows:
[tex]\[
6 \cdot \left(\frac{4}{5}\right) = \frac{6 \cdot 4}{5} = \frac{24}{5}
\][/tex]
Clearly, [tex]\(\frac{24}{5}\)[/tex] is not equal to [tex]\(\frac{4^6}{5^6}\)[/tex].
### Option B: [tex]\(\frac{4^6}{5}\)[/tex]
This expression is:
[tex]\[
\frac{4^6}{5}
\][/tex]
This is not equal to [tex]\(\frac{4^6}{5^6}\)[/tex], since the denominators are different.
### Option C: [tex]\(\frac{24}{30}\)[/tex]
This expression simplifies to:
[tex]\[
\frac{24}{30} = \frac{4}{5}
\][/tex]
This is certainly not equal to [tex]\(\frac{4^6}{5^6}\)[/tex].
### Option D: [tex]\(\frac{4^6}{5^6}\)[/tex]
This is exactly the same as our original expression:
[tex]\[
\left(\frac{4}{5}\right)^6 = \frac{4^6}{5^6}
\][/tex]
So, the correct answer is D.
The given value of [tex]\(\left(\frac{4}{5}\right)^6\)[/tex] matches only option D, [tex]\(\frac{4^6}{5^6}\)[/tex].
### Given Expression:
[tex]\[
\left(\frac{4}{5}\right)^6 = \frac{4^6}{5^6}
\][/tex]
Let's evaluate each option to see which matches this.
### Option A: [tex]\(6 \cdot \left(\frac{4}{5}\right)\)[/tex]
This expression simplifies as follows:
[tex]\[
6 \cdot \left(\frac{4}{5}\right) = \frac{6 \cdot 4}{5} = \frac{24}{5}
\][/tex]
Clearly, [tex]\(\frac{24}{5}\)[/tex] is not equal to [tex]\(\frac{4^6}{5^6}\)[/tex].
### Option B: [tex]\(\frac{4^6}{5}\)[/tex]
This expression is:
[tex]\[
\frac{4^6}{5}
\][/tex]
This is not equal to [tex]\(\frac{4^6}{5^6}\)[/tex], since the denominators are different.
### Option C: [tex]\(\frac{24}{30}\)[/tex]
This expression simplifies to:
[tex]\[
\frac{24}{30} = \frac{4}{5}
\][/tex]
This is certainly not equal to [tex]\(\frac{4^6}{5^6}\)[/tex].
### Option D: [tex]\(\frac{4^6}{5^6}\)[/tex]
This is exactly the same as our original expression:
[tex]\[
\left(\frac{4}{5}\right)^6 = \frac{4^6}{5^6}
\][/tex]
So, the correct answer is D.
The given value of [tex]\(\left(\frac{4}{5}\right)^6\)[/tex] matches only option D, [tex]\(\frac{4^6}{5^6}\)[/tex].
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