Answer :
To solve this problem, we need to determine which option is equal to the expression [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
Let's break down each option:
A. [tex]\(6 \bullet \binom{4}{5}\)[/tex]:
This option means 6 times [tex]\(\frac{4}{5}\)[/tex], which is equal to [tex]\[\frac{24}{5}.\][/tex]
This is not equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
B. [tex]\(\frac{4^6}{5^6}\)[/tex]:
This option can be rewritten as [tex]\(\left(\frac{4}{5}\right)^6\)[/tex], which matches exactly the expression we started with.
C. [tex]\(\frac{4^6}{5}\)[/tex]:
This would only be the same as [tex]\(\left(\frac{4}{5}\right)^6\)[/tex] if the denominator was also [tex]\(5^6\)[/tex], not just 5. Thus, this is not the correct option.
D. [tex]\(\frac{24}{30}\)[/tex]:
This simplifies to [tex]\(\frac{4}{5}\)[/tex], but it's certainly not raised to the sixth power. Therefore, it is not equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
Therefore, the correct answer is Option B: [tex]\(\frac{4^6}{5^6}\)[/tex].
Let's break down each option:
A. [tex]\(6 \bullet \binom{4}{5}\)[/tex]:
This option means 6 times [tex]\(\frac{4}{5}\)[/tex], which is equal to [tex]\[\frac{24}{5}.\][/tex]
This is not equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
B. [tex]\(\frac{4^6}{5^6}\)[/tex]:
This option can be rewritten as [tex]\(\left(\frac{4}{5}\right)^6\)[/tex], which matches exactly the expression we started with.
C. [tex]\(\frac{4^6}{5}\)[/tex]:
This would only be the same as [tex]\(\left(\frac{4}{5}\right)^6\)[/tex] if the denominator was also [tex]\(5^6\)[/tex], not just 5. Thus, this is not the correct option.
D. [tex]\(\frac{24}{30}\)[/tex]:
This simplifies to [tex]\(\frac{4}{5}\)[/tex], but it's certainly not raised to the sixth power. Therefore, it is not equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
Therefore, the correct answer is Option B: [tex]\(\frac{4^6}{5^6}\)[/tex].
