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Problem 86

Algebra Difficulty 1.2 Multiple choice CEMC Cayley · Canada · 2015

If $a^2 = 9$ , then $a^4$ equals

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Official solution

Since $a^2=9$ , then $a^4 = (a^2)^2 = 9^2 = 81$ .

Alternatively, we note that since $a^2 = 9$ , then $a = \pm 3$ . If $a=3$ , then $a^4 = 3^4 = 81$ and if $a=-3$ , then $a^4 = (-3)^4 = 3^4 = 81$ .

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.