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Answer :
To solve the problem, we need to understand what [tex]\((\frac{4}{5})^6\)[/tex] means. This expression represents a fraction raised to a power, which involves raising both the numerator and the denominator to that power.
Let's break it down:
1. Start with the fraction [tex]\(\frac{4}{5}\)[/tex].
2. Raise both the numerator (4) and the denominator (5) to the power of 6:
[tex]\[
\frac{4^6}{5^6}
\][/tex]
Now, let's examine each of the answer choices to find which one matches [tex]\((\frac{4}{5})^6\)[/tex]:
A. [tex]\(\frac{4^6}{5}\)[/tex]
- This is not correct because only the numerator is raised to the 6th power, and the denominator is just 5, not [tex]\(5^6\)[/tex].
B. [tex]\(\frac{24}{30}\)[/tex]
- This fraction simplifies to [tex]\(\frac{4}{5}\)[/tex], but it is not raised to any power, so it doesn't match the expression [tex]\((\frac{4}{5})^6\)[/tex].
C. [tex]\(\frac{4^{\circ}}{5^6}\)[/tex]
- This choice contains a notation error ([tex]\(4^{\circ}\)[/tex] ) and does not match our original expression.
D. [tex]\(6 \bullet (\frac{4}{5})\)[/tex]
- This represents multiplying 6 by [tex]\(\frac{4}{5}\)[/tex], not raising [tex]\(\frac{4}{5}\)[/tex] to any power.
By reviewing each option, none of the options are exactly equivalent to [tex]\((\frac{4}{5})^6 = \frac{4^6}{5^6}\)[/tex].
Since our calculated result for [tex]\((\frac{4}{5})^6\)[/tex] is approximately 0.262144, it's clear that this precise value does not match any of the provided answer choices. Therefore, there appears to be some issue as none of these options are equivalent to [tex]\((\frac{4}{5})^6\)[/tex] based on the calculation.
Let's break it down:
1. Start with the fraction [tex]\(\frac{4}{5}\)[/tex].
2. Raise both the numerator (4) and the denominator (5) to the power of 6:
[tex]\[
\frac{4^6}{5^6}
\][/tex]
Now, let's examine each of the answer choices to find which one matches [tex]\((\frac{4}{5})^6\)[/tex]:
A. [tex]\(\frac{4^6}{5}\)[/tex]
- This is not correct because only the numerator is raised to the 6th power, and the denominator is just 5, not [tex]\(5^6\)[/tex].
B. [tex]\(\frac{24}{30}\)[/tex]
- This fraction simplifies to [tex]\(\frac{4}{5}\)[/tex], but it is not raised to any power, so it doesn't match the expression [tex]\((\frac{4}{5})^6\)[/tex].
C. [tex]\(\frac{4^{\circ}}{5^6}\)[/tex]
- This choice contains a notation error ([tex]\(4^{\circ}\)[/tex] ) and does not match our original expression.
D. [tex]\(6 \bullet (\frac{4}{5})\)[/tex]
- This represents multiplying 6 by [tex]\(\frac{4}{5}\)[/tex], not raising [tex]\(\frac{4}{5}\)[/tex] to any power.
By reviewing each option, none of the options are exactly equivalent to [tex]\((\frac{4}{5})^6 = \frac{4^6}{5^6}\)[/tex].
Since our calculated result for [tex]\((\frac{4}{5})^6\)[/tex] is approximately 0.262144, it's clear that this precise value does not match any of the provided answer choices. Therefore, there appears to be some issue as none of these options are equivalent to [tex]\((\frac{4}{5})^6\)[/tex] based on the calculation.
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