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Answer :
To determine which option is equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex], let's analyze each choice:
1. Expression: [tex]\(\left(\frac{4}{5}\right)^6\)[/tex] is calculated by raising both the numerator and the denominator to the power of 6. So, it can be represented as:
[tex]\[
\frac{4^6}{5^6}
\][/tex]
2. Option A: [tex]\(\frac{24}{30}\)[/tex]
This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 6:
[tex]\[
\frac{24}{30} = \frac{24 \div 6}{30 \div 6} = \frac{4}{5}
\][/tex]
[tex]\(\frac{4}{5}\)[/tex] does not equal [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
3. Option B: [tex]\(\frac{4^6}{5^6}\)[/tex]
As previously mentioned, the expression [tex]\(\left(\frac{4}{5}\right)^6\)[/tex] is equivalent to this expression:
[tex]\[
\frac{4^6}{5^6}
\][/tex]
They are equal.
4. Option C: [tex]\(\frac{4^8}{5}\)[/tex]
This option is not equivalent to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex] since in [tex]\(\left(\frac{4}{5}\right)^6\)[/tex], both the numerator and the denominator are raised to the same power.
5. Option D: [tex]\(6 \cdot \left(\frac{4}{5}\right)\)[/tex]
This represents multiplying [tex]\(\frac{4}{5}\)[/tex] by 6:
[tex]\[
6 \cdot \frac{4}{5} = \frac{24}{5}
\][/tex]
This is clearly not the same as [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
Therefore, the option that is equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex] is Option B: [tex]\(\frac{4^6}{5^6}\)[/tex].
1. Expression: [tex]\(\left(\frac{4}{5}\right)^6\)[/tex] is calculated by raising both the numerator and the denominator to the power of 6. So, it can be represented as:
[tex]\[
\frac{4^6}{5^6}
\][/tex]
2. Option A: [tex]\(\frac{24}{30}\)[/tex]
This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 6:
[tex]\[
\frac{24}{30} = \frac{24 \div 6}{30 \div 6} = \frac{4}{5}
\][/tex]
[tex]\(\frac{4}{5}\)[/tex] does not equal [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
3. Option B: [tex]\(\frac{4^6}{5^6}\)[/tex]
As previously mentioned, the expression [tex]\(\left(\frac{4}{5}\right)^6\)[/tex] is equivalent to this expression:
[tex]\[
\frac{4^6}{5^6}
\][/tex]
They are equal.
4. Option C: [tex]\(\frac{4^8}{5}\)[/tex]
This option is not equivalent to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex] since in [tex]\(\left(\frac{4}{5}\right)^6\)[/tex], both the numerator and the denominator are raised to the same power.
5. Option D: [tex]\(6 \cdot \left(\frac{4}{5}\right)\)[/tex]
This represents multiplying [tex]\(\frac{4}{5}\)[/tex] by 6:
[tex]\[
6 \cdot \frac{4}{5} = \frac{24}{5}
\][/tex]
This is clearly not the same as [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
Therefore, the option that is equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex] is Option B: [tex]\(\frac{4^6}{5^6}\)[/tex].
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