Answer :
We start with the expression
[tex]$$
\left(\frac{4}{5}\right)^6.
$$[/tex]
Using the exponent rule for fractions, which states that
[tex]$$
\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n},
$$[/tex]
we can rewrite the expression as
[tex]$$
\left(\frac{4}{5}\right)^6 = \frac{4^6}{5^6}.
$$[/tex]
This result matches option D exactly.
For further clarity, we compute the powers:
- The numerator is
[tex]$$
4^6 = 4096.
$$[/tex]
- The denominator is
[tex]$$
5^6 = 15625.
$$[/tex]
Thus,
[tex]$$
\left(\frac{4}{5}\right)^6 = \frac{4096}{15625}.
$$[/tex]
Since this is equivalent to [tex]$\frac{4^6}{5^6}$[/tex], the correct answer is option D.
[tex]$$
\left(\frac{4}{5}\right)^6.
$$[/tex]
Using the exponent rule for fractions, which states that
[tex]$$
\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n},
$$[/tex]
we can rewrite the expression as
[tex]$$
\left(\frac{4}{5}\right)^6 = \frac{4^6}{5^6}.
$$[/tex]
This result matches option D exactly.
For further clarity, we compute the powers:
- The numerator is
[tex]$$
4^6 = 4096.
$$[/tex]
- The denominator is
[tex]$$
5^6 = 15625.
$$[/tex]
Thus,
[tex]$$
\left(\frac{4}{5}\right)^6 = \frac{4096}{15625}.
$$[/tex]
Since this is equivalent to [tex]$\frac{4^6}{5^6}$[/tex], the correct answer is option D.
