Question

Tính

a)\(\left(5^{-5}\right)^{-1}.\left(\dfrac{1}{2}\right)^{-2}.\dfrac{1}{10^5}\)

b) \(\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)

c) \(\dfrac{4^2.25^2+32.125}{2^3.5^2}\)

Answer 1

a, (5^-5)^-1 . \(\left(\dfrac{1}{2}\right)^{-2}\) . \(\dfrac{1}{10^5}\)

= 5⁵ . \(\dfrac{1^{-2}}{2^{-2}}\) . \(\dfrac{1}{10^5}\)

= (5⁵ . \(\dfrac{1}{10^5}\)) . \(\dfrac{1}{4}\)

= \(\dfrac{5^5}{10^5}\) . \(\dfrac{1}{4}\) = \(\left(\dfrac{1}{2}\right)^5\). \(\dfrac{1}{4}\)

= \(\dfrac{1}{32}.\text{​​}\dfrac{1}{4}\)= \(\dfrac{1}{128}\)

Answer 2

b: \(=\dfrac{2^{12}\cdot3^{10}+2^{12}\cdot3^{10}\cdot5}{2^{12}\cdot3^{12}-2^{11}\cdot3^{11}}\)

\(=\dfrac{2^{13}\cdot3^{11}}{2^{11}\cdot3^{11}\left(2\cdot3-1\right)}=\dfrac{4}{5}\)

c: \(=\dfrac{2^4\cdot5^4+2^5\cdot5^3}{2^3\cdot5^2}=\dfrac{2^4\cdot5^3\left(5+2\right)}{2^3\cdot5^2}=10\cdot7=70\)