JEE MAIN - Mathematics (2023 - 13th April Morning Shift - No. 11)
Fractional part of the number $$\frac{4^{2022}}{15}$$ is equal to
$$\frac{8}{15}$$
$$\frac{4}{15}$$
$$\frac{1}{15}$$
$$\frac{14}{15}$$
Explanation
$$
\begin{aligned}
& \left\{\frac{4^{2022}}{15}\right\}=\left\{\frac{2^{4044}}{15}\right\} \\\\
& =\left\{\frac{(1+15)^{1011}}{15}\right\} \\\\
& =\frac{1}{15}
\end{aligned}
$$
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