Question

Answer 1

1:

a: \(\dfrac{2^{30}\cdot5^7+2^{13}\cdot5^{27}}{2^{27}\cdot5^7+2^{10}\cdot5^{27}}\)

\(=\dfrac{2^{13}\cdot5^7\left(2^{17}+5^{20}\right)}{2^{10}\cdot5^7\left(2^{17}+5^{20}\right)}=2^3=8\)

b: \(\left(\dfrac{9}{15}\right)^{2022}\cdot\left(\dfrac{15}{9}\right)^{2021}\)

\(=\left(\dfrac{3}{5}\right)^{2022}\cdot\left(\dfrac{5}{3}\right)^{2021}\)

\(=\left(\dfrac{3}{5}\right)\cdot\left(\dfrac{3}{5}\right)^{2021}\cdot\left(\dfrac{5}{3}\right)^{2021}\)

\(=\dfrac{3}{5}\cdot\left(\dfrac{3}{5}\cdot\dfrac{5}{3}\right)^{2021}=\dfrac{3}{5}\)