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.
[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.
