Question

For what value of a does (one-ninth) Superscript a + 1 Baseline = 81 Superscript a + 1 Baseline times 27 Superscript 2 minus a?
–4
–2
2
6

Answer 1

Convert to base 3:

(1/9)^{a+1} = 3^{-2(a+1)} = 3^{-2a-2}.

81^{a+1}·27^{2-a} = 3^{4(a+1)}·3^{3(2-a)} = 3^{4a+4+6-3a} = 3^{a+10}.

So -2a-2 = a+10 → -3a = 12 → a = -4.

Answer: -4.