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

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.

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