Given: A= 3^n - 4/ 6^n - 2^n+2 (n+2 are both exponential to 2)

Question

1) Simplify A 2) Hence determine n^√A

Answer 1

(1)

A=(3ⁿ-4)/(6ⁿ-2ⁿ⁺²) (assuming this is what is meant).

6ⁿ-2ⁿ⁺²=2ⁿ3ⁿ-4×2ⁿ=2ⁿ(3ⁿ-4), so A=1/2ⁿ or 2⁻ⁿ.

(2) √A=2^(-n/2), n^(√A)=n^(2^(-n/2)).

Examples:

If n=2, n^(√A)=2^(2⁻¹)=2^½=√2.

If n=3, n^(√A)=3^(2^(-3/2)).

If n=4, n^(√A)=4^(2⁻²)=4^¼=√2.

Comments

He would had gotten the help much earlier, if he was clear about the question.

I was banging my head against this equation.

A=3ⁿ-(4/6ⁿ)-2ⁿ⁺²

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Part of this game is translating questions into something that’s meaningful! And sometimes there are errors and/or ambiguities in the question which have to be corrected before the question can be answered. In some cases I’ve answered a question by trying to interpret and then answer all possible interpretations of ambiguities.

In this question I fiddled with a couple of interpretations until I found one which enabled me to simplify A. I’m not so sure about the second part, so I just answered it plainly.