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Answer :
To solve the problem, we need to determine which option is equal to the expression [tex]\( \left(\frac{4}{5}\right)^6 \)[/tex].
Let's break down each option:
Option A: [tex]\(\frac{24}{30}\)[/tex]
- Simplifying [tex]\(\frac{24}{30}\)[/tex], we get [tex]\(\frac{4}{5}\)[/tex] because both the numerator and denominator can be divided by 6. However, this simplified fraction isn't raised to the sixth power as required by the original expression. So, it doesn't match [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
Option B: [tex]\(6 \bullet\left(\frac{4}{5}\right)\)[/tex]
- This option represents multiplying [tex]\(\frac{4}{5}\)[/tex] by 6. It does not involve raising [tex]\(\frac{4}{5}\)[/tex] to the power of 6, as required by the original expression. Thus, this does not equal [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
Option C: [tex]\(\frac{4^6}{5^6}\)[/tex]
- The expression [tex]\(\frac{4^6}{5^6}\)[/tex] is another way of writing [tex]\(\left(\frac{4}{5}\right)^6\)[/tex]. When you raise a fraction to a power, you individually raise the numerator and the denominator to that power. So, this option is indeed equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
Option D: [tex]\(\frac{4^6}{5}\)[/tex]
- This option only raises the numerator to the sixth power, leaving the denominator as 5, not [tex]\(5^6\)[/tex]. Therefore, this does not correspond to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
After evaluating all options, we see that Option C: [tex]\(\frac{4^6}{5^6}\)[/tex] is equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
Let's break down each option:
Option A: [tex]\(\frac{24}{30}\)[/tex]
- Simplifying [tex]\(\frac{24}{30}\)[/tex], we get [tex]\(\frac{4}{5}\)[/tex] because both the numerator and denominator can be divided by 6. However, this simplified fraction isn't raised to the sixth power as required by the original expression. So, it doesn't match [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
Option B: [tex]\(6 \bullet\left(\frac{4}{5}\right)\)[/tex]
- This option represents multiplying [tex]\(\frac{4}{5}\)[/tex] by 6. It does not involve raising [tex]\(\frac{4}{5}\)[/tex] to the power of 6, as required by the original expression. Thus, this does not equal [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
Option C: [tex]\(\frac{4^6}{5^6}\)[/tex]
- The expression [tex]\(\frac{4^6}{5^6}\)[/tex] is another way of writing [tex]\(\left(\frac{4}{5}\right)^6\)[/tex]. When you raise a fraction to a power, you individually raise the numerator and the denominator to that power. So, this option is indeed equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
Option D: [tex]\(\frac{4^6}{5}\)[/tex]
- This option only raises the numerator to the sixth power, leaving the denominator as 5, not [tex]\(5^6\)[/tex]. Therefore, this does not correspond to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
After evaluating all options, we see that Option C: [tex]\(\frac{4^6}{5^6}\)[/tex] is equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
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