Question

a) \(\left(1,25\right)^3.8^3\)

b) \(\left(\dfrac{-11}{9}\right)^4.\left(\dfrac{27}{22}\right)^4\)

c) \(\left(\dfrac{3}{7}+\dfrac{1}{2}\right)^2\)

d) \(\dfrac{5^4.20^4}{25^5.4^5}\)

Answer 1

a) \(\left(1,25\right)^3.8^3=\left(1,25.8\right)^3=1000\)

b) \(\left(\dfrac{-11}{9}\right)^4.\left(\dfrac{27}{22}\right)^4=\left(\dfrac{-11}{9}.\dfrac{27}{22}\right)^4=\left(\dfrac{-11.9.3}{9.2.\left(-11\right)}\right)^4\)

\(=\left(\dfrac{3}{2}\right)^4=\dfrac{81}{16}\)

c) \(\left(\dfrac{3}{7}+\dfrac{1}{2}\right)^2=\left(\dfrac{13}{14}\right)^2=\dfrac{169}{196}\)

d) \(\dfrac{5^4.20^4}{25^5.4^5}=\dfrac{\left(5.20\right)^4}{\left(25.4\right)^5}=\dfrac{100^4}{100^5}=100^{-1}=0,01\)