Maths Olympiad Prep

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Algebra Difficulty 1.8 Junior Find the answer

What is the expression 23+22+212^{3}+2^{2}+2^{1} equal to?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Since 21=22^{1}=2 and 22=2imes2=42^{2}=2 imes 2=4 and 23=2imes2imes2=82^{3}=2 imes 2 imes 2=8, then 23+22+21=8+4+2=142^{3}+2^{2}+2^{1}=8+4+2=14.

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