Question

Find the remainder when ${42}^{442}$ is divided by 100.
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Answer 1

Using the last two digits technique -

${42}^{442}=(21\times 2{)}^{442}$

$=(21{)}^{442}\times (2{)}^{442}=(21{)}^{442}\times (2^{44}{)}^{10}\times 2^2=\_\_41\times \_\_76\times \_\_04=\_\_41\times \_\_04=\_\_64.$