Maths Olympiad Prep

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Algebra Difficulty 2.1 Junior Find the answer

Which of the following is equal to 949^{4}?

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

Solution

Since 9=3×39=3 \times 3, then 94=(3×3)4=34×34=389^{4}=(3 \times 3)^{4}=3^{4} \times 3^{4}=3^{8}. Alternatively, we can note that 94=9×9×9×9=(3×3)×(3×3)×(3×3)×(3×3)=389^{4}=9 \times 9 \times 9 \times 9=(3 \times 3) \times(3 \times 3) \times(3 \times 3) \times(3 \times 3)=3^{8}.

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