Answer :
To solve the question of which expression is equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex], let's carefully examine each option:
Given expression:
[tex]\[
\left(\frac{4}{5}\right)^6
\][/tex]
Let's look at each option:
Option A: [tex]\(\frac{4^6}{5}\)[/tex]
- This option suggests raising 4 to the power of 6 and then dividing it by 5. This is not the same as raising the whole fraction [tex]\(\frac{4}{5}\)[/tex] to the power of 6.
Option B: [tex]\(\frac{24}{30}\)[/tex]
- The fraction [tex]\(\frac{24}{30}\)[/tex] simplifies to [tex]\(\frac{4}{5}\)[/tex], but not when raised to the power of 6. Therefore, this option does not match [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
Option C: [tex]\(6 \bullet \left(\frac{4}{5}\right)\)[/tex]
- This option suggests multiplying the fraction [tex]\(\frac{4}{5}\)[/tex] by 6. This is not the same as raising [tex]\(\frac{4}{5}\)[/tex] to the power of 6.
Option D: [tex]\(\frac{4^6}{5^6}\)[/tex]
- This option shows each part of the fraction being raised to the power of 6. This is equivalent to raising the entire fraction [tex]\(\frac{4}{5}\)[/tex] to the power of 6. Thus, this matches the original expression.
From this analysis, Option D, [tex]\(\frac{4^6}{5^6}\)[/tex], is the correct answer since it correctly represents the expression [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
Given expression:
[tex]\[
\left(\frac{4}{5}\right)^6
\][/tex]
Let's look at each option:
Option A: [tex]\(\frac{4^6}{5}\)[/tex]
- This option suggests raising 4 to the power of 6 and then dividing it by 5. This is not the same as raising the whole fraction [tex]\(\frac{4}{5}\)[/tex] to the power of 6.
Option B: [tex]\(\frac{24}{30}\)[/tex]
- The fraction [tex]\(\frac{24}{30}\)[/tex] simplifies to [tex]\(\frac{4}{5}\)[/tex], but not when raised to the power of 6. Therefore, this option does not match [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
Option C: [tex]\(6 \bullet \left(\frac{4}{5}\right)\)[/tex]
- This option suggests multiplying the fraction [tex]\(\frac{4}{5}\)[/tex] by 6. This is not the same as raising [tex]\(\frac{4}{5}\)[/tex] to the power of 6.
Option D: [tex]\(\frac{4^6}{5^6}\)[/tex]
- This option shows each part of the fraction being raised to the power of 6. This is equivalent to raising the entire fraction [tex]\(\frac{4}{5}\)[/tex] to the power of 6. Thus, this matches the original expression.
From this analysis, Option D, [tex]\(\frac{4^6}{5^6}\)[/tex], is the correct answer since it correctly represents the expression [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
