Question

Tính:

\(A=\dfrac{27^{10}+9^5}{9^{13}+27^2}\)

Answer 1

\(A=\dfrac{27^{10}+9^5}{9^{13}+27^2}\\ =\dfrac{\left(3^3\right)^{10}+\left(3^2\right)^5}{\left(3^2\right)^{13}+\left(3^3\right)^2}\\ =\dfrac{3^{30}+3^{10}}{3^{26}+3^6}\\ =\dfrac{3^{10}\left(3^{20}+1\right)}{3^6\left(3^{20}+1\right)}\\ =\dfrac{3^{10}}{3^6}\\=3^4\\ =81\)

Answer 2

\(A=\dfrac{27^{10}+9^5}{9^{13}+27^2}\)

\(A=\dfrac{\left(3^3\right)^{10}+\left(3^2\right)^5}{\left(3^2\right)^{13}+\left(3^3\right)^2}\)

\(A=\dfrac{3^{30}+3^{10}}{3^{26}+3^6}\)

\(A=\dfrac{3^{10}+\left(3^{20}+1\right)}{3^6.\left(3^{20}+1\right)}\)

\(A=\dfrac{3^{10}}{3^6}\)

\(A=3^4\)

\(A=81\)