Answer :
To solve this question, we need to understand how to work with powers of fractions:
1. Understand the Expression: We are looking at [tex]\((\frac{4}{5})^6\)[/tex]. When we raise a fraction to a power, both the numerator and the denominator are raised to that power.
2. Apply the Rule: For [tex]\((\frac{4}{5})^6\)[/tex], this means the numerator 4 and the denominator 5 are each raised to the power of 6. This gives us:
[tex]\[
(\frac{4}{5})^6 = \frac{4^6}{5^6}
\][/tex]
3. Match with the Given Options: From the given options, we are looking for one that matches [tex]\(\frac{4^6}{5^6}\)[/tex].
- Option A: [tex]\(\frac{24}{30}\)[/tex] - This is a simplified fraction and does not match [tex]\(\frac{4^6}{5^6}\)[/tex].
- Option B: [tex]\(6 \cdot(\frac{4}{5})\)[/tex] - This involves multiplication by 6, not raising to the sixth power.
- Option C: [tex]\(\frac{4^6}{5^6}\)[/tex] - This is exactly what we calculated.
- Option D: [tex]\(\frac{4^6}{5}\)[/tex] - This does not raise 5 to the sixth power.
Therefore, the expression [tex]\((\frac{4}{5})^6\)[/tex] is equal to [tex]\(\frac{4^6}{5^6}\)[/tex], which corresponds to option C.
1. Understand the Expression: We are looking at [tex]\((\frac{4}{5})^6\)[/tex]. When we raise a fraction to a power, both the numerator and the denominator are raised to that power.
2. Apply the Rule: For [tex]\((\frac{4}{5})^6\)[/tex], this means the numerator 4 and the denominator 5 are each raised to the power of 6. This gives us:
[tex]\[
(\frac{4}{5})^6 = \frac{4^6}{5^6}
\][/tex]
3. Match with the Given Options: From the given options, we are looking for one that matches [tex]\(\frac{4^6}{5^6}\)[/tex].
- Option A: [tex]\(\frac{24}{30}\)[/tex] - This is a simplified fraction and does not match [tex]\(\frac{4^6}{5^6}\)[/tex].
- Option B: [tex]\(6 \cdot(\frac{4}{5})\)[/tex] - This involves multiplication by 6, not raising to the sixth power.
- Option C: [tex]\(\frac{4^6}{5^6}\)[/tex] - This is exactly what we calculated.
- Option D: [tex]\(\frac{4^6}{5}\)[/tex] - This does not raise 5 to the sixth power.
Therefore, the expression [tex]\((\frac{4}{5})^6\)[/tex] is equal to [tex]\(\frac{4^6}{5^6}\)[/tex], which corresponds to option C.
