Exercice 1

Calculer à la main

Question

\((3^4)^2  ; 4^2 - 4^3  ; 2 × 7^2 - 7 × 2^2\)

Solution

\((3^4)^2 = 6561  ; 4^2 - 4^3 = -48  ; 2 × 7^2 - 7 × 2^2 = 70\)

Question

\(\left(\frac{3}{2}\right)^3  ; \frac{125^2}{5^4}  ; \frac{18^2}{45^2} \)

Solution

\(\left(\frac{3}{2}\right)^3 = \frac{27}{8}  ; \frac{125^2}{5^4} = 25 ; \frac{18^2}{45^2} = \frac{4}{25}\)

Question

\(\left(\frac{3^4}{3^6}\right)^2  ; (3^{-4})^5  ; (3^{-6})^{-2}  ; \frac{5^{-2}× (3^{4})^2 }{(5^{-2} × 3^3)^3}\)

Solution

\(\left(\frac{3^4}{3^6}\right)^2 = \frac{1}{81} ; (3^{-4})^5 = \frac{1}{3486784401}  ; (3^{-6})^{-2} =  531441 ; \frac{5^{-2}× (3^{4})^2 }{(5^{-2} × 3^3)^3} = \frac{25}{3}\)