Answer :
Sure, let's work through the problem step by step.
We need to determine which option is equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
First, let's rewrite the expression in different forms to see which option matches.
The expression [tex]\(\left(\frac{4}{5}\right)^6\)[/tex] can be expanded as follows:
[tex]\[
\left(\frac{4}{5}\right)^6 = \frac{4^6}{5^6}
\][/tex]
Now, let's compare this with each of the given options:
Option A: [tex]\(\frac{4^6}{5}\)[/tex]
- This is not correct because the denominator should be [tex]\(5^6\)[/tex], not [tex]\(5\)[/tex].
Option B: [tex]\(6 \cdot \left(\frac{4}{5}\right)\)[/tex]
- This is not correct because the original expression involves raising the fraction to the 6th power, not simply multiplying by 6.
Option C: [tex]\(\frac{4^6}{5^6}\)[/tex]
- This matches perfectly because it keeps the expression in the same form.
Option D: [tex]\(\frac{24}{30}\)[/tex]
- Simplifying [tex]\(\frac{24}{30}\)[/tex] gives [tex]\(\frac{4}{5}\)[/tex], which is not equivalent to raising [tex]\(\frac{4}{5}\)[/tex] to the 6th power.
Hence, the correct answer is:
C. [tex]\(\frac{4^6}{5^6}\)[/tex]
We need to determine which option is equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
First, let's rewrite the expression in different forms to see which option matches.
The expression [tex]\(\left(\frac{4}{5}\right)^6\)[/tex] can be expanded as follows:
[tex]\[
\left(\frac{4}{5}\right)^6 = \frac{4^6}{5^6}
\][/tex]
Now, let's compare this with each of the given options:
Option A: [tex]\(\frac{4^6}{5}\)[/tex]
- This is not correct because the denominator should be [tex]\(5^6\)[/tex], not [tex]\(5\)[/tex].
Option B: [tex]\(6 \cdot \left(\frac{4}{5}\right)\)[/tex]
- This is not correct because the original expression involves raising the fraction to the 6th power, not simply multiplying by 6.
Option C: [tex]\(\frac{4^6}{5^6}\)[/tex]
- This matches perfectly because it keeps the expression in the same form.
Option D: [tex]\(\frac{24}{30}\)[/tex]
- Simplifying [tex]\(\frac{24}{30}\)[/tex] gives [tex]\(\frac{4}{5}\)[/tex], which is not equivalent to raising [tex]\(\frac{4}{5}\)[/tex] to the 6th power.
Hence, the correct answer is:
C. [tex]\(\frac{4^6}{5^6}\)[/tex]
