Simplify :
5n+3−6×5n+19×5n−5n×22\dfrac{5^{n + 3} - 6 \times 5^{n + 1}}{9 \times 5^n - 5^n \times 2^2}9×5n−5n×225n+3−6×5n+1
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Simplifying the expression :
⇒5n+3−6×5n+19×5n−5n×22=5n.53−6×5n×515n(9−22)=5n(53−6×5)5n(9−4)=125−305=955=19.\Rightarrow \dfrac{5^{n + 3} - 6 \times 5^{n + 1}}{9 \times 5^n - 5^n \times 2^2} = \dfrac{5^n.5^3 - 6 \times 5^n \times 5^1}{5^n(9 - 2^2)} \\[1em] = \dfrac{5^n(5^3 - 6 \times 5)}{5^n(9 - 4)} = \dfrac{125 - 30}{5} = \dfrac{95}{5} \\[1em] = 19.⇒9×5n−5n×225n+3−6×5n+1=5n(9−22)5n.53−6×5n×51=5n(9−4)5n(53−6×5)=5125−30=595=19.
Hence, 5n+3−6×5n+19×5n−5n×22=19.\dfrac{5^{n + 3} - 6 \times 5^{n + 1}}{9 \times 5^n - 5^n \times 2^2} = 19.9×5n−5n×225n+3−6×5n+1=19.
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(8x3÷125y3)23(8x^3 ÷ 125y^3)^{\dfrac{2}{3}}(8x3÷125y3)32
(a + b)-1.(a-1 + b-1)
(3x2)−3×(x9)23(3x^2)^{-3} \times (x^9)^{\dfrac{2}{3}}(3x2)−3×(x9)32
Evaluate :
14+(0.01)−12−(27)23\sqrt{\dfrac{1}{4}} + (0.01)^{-\dfrac{1}{2}} - (27)^{\dfrac{2}{3}}41+(0.01)−21−(27)32
