Answer :
To determine which option is equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex], let's look at each option one by one:
1. Option A: [tex]\(\frac{4^6}{5^6}\)[/tex]
- When you raise a fraction to a power, you can apply the power to both the numerator and the denominator. So, [tex]\(\left(\frac{4}{5}\right)^6\)[/tex] is equal to [tex]\(\frac{4^6}{5^6}\)[/tex].
2. Option B: [tex]\(\frac{24}{30}\)[/tex]
- Simplifying [tex]\(\frac{24}{30}\)[/tex], we get [tex]\(\frac{4}{5}\)[/tex]. However, [tex]\(\frac{4}{5}\)[/tex] is not equivalent to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
3. Option C: [tex]\(\frac{4^6}{5}\)[/tex]
- This expression does not apply the power of 6 correctly because only the numerator is raised to the sixth power, not the entire fraction.
4. Option D: [tex]\(6 \cdot \left(\frac{4}{5}\right)\)[/tex]
- This expression represents 6 times the fraction [tex]\(\frac{4}{5}\)[/tex], which is not equivalent to raising [tex]\(\frac{4}{5}\)[/tex] to the sixth power.
Based on evaluating these options, Option A: [tex]\(\frac{4^6}{5^6}\)[/tex] is equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
1. Option A: [tex]\(\frac{4^6}{5^6}\)[/tex]
- When you raise a fraction to a power, you can apply the power to both the numerator and the denominator. So, [tex]\(\left(\frac{4}{5}\right)^6\)[/tex] is equal to [tex]\(\frac{4^6}{5^6}\)[/tex].
2. Option B: [tex]\(\frac{24}{30}\)[/tex]
- Simplifying [tex]\(\frac{24}{30}\)[/tex], we get [tex]\(\frac{4}{5}\)[/tex]. However, [tex]\(\frac{4}{5}\)[/tex] is not equivalent to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
3. Option C: [tex]\(\frac{4^6}{5}\)[/tex]
- This expression does not apply the power of 6 correctly because only the numerator is raised to the sixth power, not the entire fraction.
4. Option D: [tex]\(6 \cdot \left(\frac{4}{5}\right)\)[/tex]
- This expression represents 6 times the fraction [tex]\(\frac{4}{5}\)[/tex], which is not equivalent to raising [tex]\(\frac{4}{5}\)[/tex] to the sixth power.
Based on evaluating these options, Option A: [tex]\(\frac{4^6}{5^6}\)[/tex] is equal to [tex]\(\left(\frac{4}{5}\right)^6\)[/tex].
