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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{24}{30}[/tex]
B. [tex]\frac{4^6}{5}[/tex]
C. [tex]6 \cdot\left(\frac{4}{5}\right)[/tex]
D. [tex]\frac{4^6}{5^6}[/tex]

Answer :

To solve the problem, we start by recognizing that when a fraction is raised to a power, both the numerator and the denominator are raised to that power. Therefore, we have:

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

Now, comparing this result to the given options, we see that option D is:

[tex]$$
\frac{4^6}{5^6},
$$[/tex]

which is exactly the same as the expression we derived.

Thus, the correct answer is option D.