Question

Write as a power of 3


`\frac{ {3}^(n) }{ {9}^(n - 1) }`
Please help, many thanks

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Answer 1

3⁻ⁿ⁺²

Explanation:

we need to make both bases the same

9 can be written as 3²

`\frac{3 {}^(n) }{3 {}^(2(n - 1)) }`

multiply 2(n-1) = 2n - 2

`\frac{3 {}^(n) }{3 {}^(2n - 2) }`

I'll rewrite as 3ⁿ ÷ 3²ⁿ⁻²

subtract the exponents when dividing numbers with the same base

n - (2n-2) or n - 1(2n-2) imagine the 1 is there

remember that the whole of (2n-2) is being multiplied by -1, so expanding

n - 2n + 2 = -n + 2

final answer: 3⁻ⁿ⁺²