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------------------------------------------------ Which of the following is equal to the fraction below?

[tex]\left(\frac{4}{5}\right)^6[/tex]

A. [tex]\frac{4^6}{5^6}[/tex]

B. [tex]\frac{24}{30}[/tex]

C. [tex]\frac{4^6}{5}[/tex]

D. [tex]6 \cdot \left(\frac{4}{5}\right)[/tex]

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].