Simplify (9^n + 1 × 3^2n - 1)/81^n.

Simplification & Approximation · Question 49 of 71

Question 49

MediumOriginal question

Simplify $\dfrac{9^{n + 1} \times 3^{2n - 1}}{81^{n}}$ .

\frac{1}{9}

Correct answerYour answer

\frac{1}{3}

Correct answerYour answer1Correct answerYour answer3Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Write every base as a power of 3: $9^{n + 1} = 3^{2n + 2}$ and $81^n = 3^{4n}$ .
Numerator: $3^{2n + 2} \times 3^{2n - 1} = 3^{4n + 1}$ .
Divide: $3^{4n + 1 - 4n} = 3^1 = 3$ .

Worth noting

Writing $9^{n + 1}$ as $3^{2n + 1}$ (forgetting to double the 1) gives $3^0 = 1$ . Double the whole exponent.

Ten questions from Simplification & Approximation, at your own pace.

Ten questions from Simplification & Approximation, at your own pace.