Question

\(\frac{2^{15}.9^4}{6^6.8^3}\)

Answer 1

\(\frac{2^{15}\cdot9^4}{6^6\cdot8^3}=\frac{2^{15}\cdot3^4\cdot3^4}{2^6\cdot3^6\cdot\left(2^4\right)^3}=\frac{2^{12}\cdot2^3\cdot3^8}{2^6\cdot3^6\cdot2^{12}}\)

\(=\frac{2^3\cdot3^2\cdot3^6}{2^3\cdot2^3\cdot3^6}=\frac{3^3}{2^3}\)

\(=\frac{27}{8}\)

Answer 2

\(\frac{2^{15}.9^4}{6^6.8^3}=\frac{\left(2^3\right)^5.\left(3^2\right)^4}{6^6.8^3}=\frac{8^5.3^8}{6^6.8^3}\)

\(=\frac{8^2.3^8}{6^6}=\frac{64.6561}{46656}=\frac{64.6561}{64.729}\)

\(=\frac{6561}{729}=9\)

Answer 3

\(\frac{2^{15}\cdot9^4}{6^6\cdot8^3}=\frac{2^{15}\cdot\left(3^3\right)^4}{\left(2^3\right)^3\cdot\left(2.3\right)^6}=\frac{2^{15}\cdot3^{12}}{2^9\cdot2^6\cdot3^6}=\frac{2^{15}\cdot3^{12}}{2^{15}\cdot3^6}=3^6\)