Simplify; \(\frac{3^{n - 1} \times 27^{n + 1}}{81^{n}}\)
Question 1 Report
Simplify; \(\frac{3^{n - 1} \times 27^{n + 1}}{81^{n}}\)
Answer Details
We can simplify this expression by using the properties of exponents and simplifying the numbers. First, we can write 27 as 33 and 81 as 34. Next, we can simplify the numerator by using the distributive property of exponents: \begin{align*} \frac{3^{n-1} \times 27^{n+1}}{81^n} &= \frac{3^{n-1} \times 3^{3(n+1)}}{3^{4n}} \\ &= \frac{3^{n-1} \times 3^{3n+3}}{3^{4n}} \\ &= \frac{3^{4n-1}}{3^{4n}} \times 3^{3n+3} \\ &= 3^{-1} \times 3^{3n+3} \\ &= 3^{3n+2} \\ &= 3^2 \times 3^{3n} \\ &= 9 \times 3^n \\ \end{align*} Therefore, the simplified expression is 9 * 3n. So, the answer is 9.
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