Question

Answer 1

25) \(\dfrac{9^3\cdot27^2}{6^2\cdot3^{10}}\)

\(=\dfrac{\left(3^2\right)^3\cdot\left(3^3\right)^2}{2^2\cdot3^2\cdot3^{10}}\)

\(=\dfrac{3^{12}}{2^2\cdot3^{12}}\)

\(=\dfrac{1}{2^2\cdot1}\)

\(=\dfrac{1}{4}\)

26) \(\dfrac{15^{13}\cdot4^{12}}{6^{12}\cdot10^{13}}\)

\(=\dfrac{3^{13}\cdot5^{13}\cdot\left(2^2\right)^{12}}{2^{12}\cdot3^{12}\cdot5^{13}\cdot2^{13}}\)

\(=\dfrac{3^{13}\cdot5^{13}\cdot2^{24}}{2^{25}\cdot3^{12}\cdot5^{13}}\)

\(=\dfrac{3\cdot1\cdot1}{2\cdot1\cdot1}\)

\(=\dfrac{3}{2}\)

27) \(\dfrac{2^4\cdot2^3}{8^2}\)

\(=\dfrac{2^7}{\left(2^3\right)^2}\)

\(=\dfrac{2^7}{2^6}\)

\(=2\)