Simplify :
3n×9n+13n−1×9n−1\dfrac{3^n \times 9^{n + 1}}{3^{n - 1} \times 9^{n - 1}}3n−1×9n−13n×9n+1
2 Likes
Given,
Simplifying the expression :
⇒3n×9n+13n−1×9n−1⇒3n×(32)n+13n−1×(32)n−1⇒3n×(3)2n+23n−1×(3)2n−2⇒3n+2n+23n−1+2n−2⇒33n+233n−3⇒3(3n+2)−(3n−3)⇒3(3n+2−3n+3)⇒35.\Rightarrow \dfrac{3^n \times 9^{n + 1}}{3^{n - 1} \times 9^{n - 1}} \\[1em] \Rightarrow \dfrac{3^n \times (3^2)^{n + 1}}{3^{n - 1} \times (3^2)^{n - 1}} \\[1em] \Rightarrow \dfrac{3^n \times (3)^{2n + 2}}{3^{n - 1} \times (3)^{2n - 2}} \\[1em] \Rightarrow \dfrac{3^{n + 2n + 2}}{3^{n - 1 + 2n - 2}} \\[1em] \Rightarrow \dfrac{3^{3n + 2}}{3^{3n - 3}} \\[1em] \Rightarrow 3^{(3n + 2) - (3n - 3)} \\[1em] \Rightarrow 3^{(3n + 2 - 3n + 3)} \\[1em] \Rightarrow 3^5.⇒3n−1×9n−13n×9n+1⇒3n−1×(32)n−13n×(32)n+1⇒3n−1×(3)2n−23n×(3)2n+2⇒3n−1+2n−23n+2n+2⇒33n−333n+2⇒3(3n+2)−(3n−3)⇒3(3n+2−3n+3)⇒35.
Hence, 3n×9n+13n−1×9n−1=35\dfrac{3^n \times 9^{n + 1}}{3^{n - 1} \times 9^{n - 1}} = 3^53n−1×9n−13n×9n+1=35.
Answered By
1 Like
Evaluate the following :
(32−5)13(32+5)13(\sqrt{32}-\sqrt{5})^{\dfrac{1}{3}} (\sqrt{32}+\sqrt{5})^{\dfrac{1}{3}}(32−5)31(32+5)31
(9)52−3×(4)0−(181)−12(9)^{\dfrac{5}{2}} - 3 \times (4)^0 - \Big(\dfrac{1}{81}\Big)^{-\dfrac{1}{2}}(9)25−3×(4)0−(811)−21
(27)2n3×(8)−n6(18)−n2\dfrac{(27)^{\dfrac{2n}{3}} \times (8)^{-\dfrac{n}{6}}}{(18)^{-\dfrac{n}{2}}}(18)−2n(27)32n×(8)−6n
52(n+6)×(25)−7+2n(125)2n\dfrac{5^{2(n + 6)} \times (25)^{-7 + 2n}}{(125)^{2n}}(125)2n52(n+6)×(25)−7+2n
