Answer :
To solve this problem, we want to find which option is equal to the expression [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
Let's evaluate each option:
1. Option A: [tex]\(\frac{4^6}{5^6}\)[/tex]
- This expression is a direct match for [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
- So, [tex]\(\left(\frac{4}{5}\right)^6 = \frac{4^6}{5^6}\)[/tex].
- This option is correct.
2. Option B: [tex]\(\frac{24}{30}\)[/tex]
- Simplify [tex]\(\frac{24}{30}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, 6:
- [tex]\(\frac{24 \div 6}{30 \div 6} = \frac{4}{5}\)[/tex].
- This fraction is not the same as [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
3. Option C: [tex]\(6 \cdot \frac{4}{5}\)[/tex]
- Calculate it by multiplying: [tex]\(6 \times \frac{4}{5} = \frac{24}{5}\)[/tex].
- This is a completely different value compared to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
4. Option D: [tex]\(\frac{4^6}{5}\)[/tex]
- This represents [tex]\(4^6\)[/tex] divided by 5, not raised to the power of 6 over 5.
- This is also incorrect as it doesn’t equal [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
After evaluating each option, we can conclude that the correct answer is Option A: [tex]\(\frac{4^6}{5^6}\)[/tex], as it perfectly matches the given expression [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
Let's evaluate each option:
1. Option A: [tex]\(\frac{4^6}{5^6}\)[/tex]
- This expression is a direct match for [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
- So, [tex]\(\left(\frac{4}{5}\right)^6 = \frac{4^6}{5^6}\)[/tex].
- This option is correct.
2. Option B: [tex]\(\frac{24}{30}\)[/tex]
- Simplify [tex]\(\frac{24}{30}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, 6:
- [tex]\(\frac{24 \div 6}{30 \div 6} = \frac{4}{5}\)[/tex].
- This fraction is not the same as [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
3. Option C: [tex]\(6 \cdot \frac{4}{5}\)[/tex]
- Calculate it by multiplying: [tex]\(6 \times \frac{4}{5} = \frac{24}{5}\)[/tex].
- This is a completely different value compared to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
4. Option D: [tex]\(\frac{4^6}{5}\)[/tex]
- This represents [tex]\(4^6\)[/tex] divided by 5, not raised to the power of 6 over 5.
- This is also incorrect as it doesn’t equal [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
After evaluating each option, we can conclude that the correct answer is Option A: [tex]\(\frac{4^6}{5^6}\)[/tex], as it perfectly matches the given expression [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
