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Answer :
Let's solve the problem step by step:
We need to find which option is equal to the expression [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
Let's break down the expression:
- [tex]\(\left(\frac{4}{5}\right)^6 = \frac{4^6}{5^6}\)[/tex].
Now, we need to compare it to each option given:
A. [tex]\(\frac{4^6}{5}\)[/tex]
- This expression is not equal because the denominator in the correct expression is [tex]\(5^6\)[/tex], not [tex]\(5\)[/tex].
B. [tex]\(6 \cdot \left(\frac{4}{5}\right)\)[/tex]
- This expression represents multiplying [tex]\(\frac{4}{5}\)[/tex] by 6, which is not the same as raising it to the power of 6.
C. [tex]\(\frac{4^6}{5^6}\)[/tex]
- This matches exactly with [tex]\(\left(\frac{4}{5}\right)^6\)[/tex] since both mean raising [tex]\(\frac{4}{5}\)[/tex] to the sixth power.
D. [tex]\(\frac{24}{30}\)[/tex]
- This simplifies to [tex]\(\frac{4}{5}\)[/tex], which is the original fraction raised to the first power, not the sixth power.
Thus, the correct answer is C: [tex]\(\frac{4^6}{5^6}\)[/tex].
We need to find which option is equal to the expression [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
Let's break down the expression:
- [tex]\(\left(\frac{4}{5}\right)^6 = \frac{4^6}{5^6}\)[/tex].
Now, we need to compare it to each option given:
A. [tex]\(\frac{4^6}{5}\)[/tex]
- This expression is not equal because the denominator in the correct expression is [tex]\(5^6\)[/tex], not [tex]\(5\)[/tex].
B. [tex]\(6 \cdot \left(\frac{4}{5}\right)\)[/tex]
- This expression represents multiplying [tex]\(\frac{4}{5}\)[/tex] by 6, which is not the same as raising it to the power of 6.
C. [tex]\(\frac{4^6}{5^6}\)[/tex]
- This matches exactly with [tex]\(\left(\frac{4}{5}\right)^6\)[/tex] since both mean raising [tex]\(\frac{4}{5}\)[/tex] to the sixth power.
D. [tex]\(\frac{24}{30}\)[/tex]
- This simplifies to [tex]\(\frac{4}{5}\)[/tex], which is the original fraction raised to the first power, not the sixth power.
Thus, the correct answer is C: [tex]\(\frac{4^6}{5^6}\)[/tex].
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