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Which of the following is equal to the fraction below?

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

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

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

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

D. [tex]\(\frac{4^6}{5^6}\)[/tex]

Answer :

We start with the fraction

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

When raising a fraction to an exponent, both the numerator and the denominator are raised to that exponent. In other words, for any numbers [tex]$a$[/tex], [tex]$b$[/tex], and [tex]$n$[/tex], we have

[tex]$$
\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}.
$$[/tex]

Applying this rule with [tex]$a = 4$[/tex], [tex]$b = 5$[/tex], and [tex]$n = 6$[/tex], we get

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

Thus, the correct choice is:

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

This corresponds to option D.

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