Bonjour svp c urgent en maths

Bonjour BeautyLina

Exercice 5

[tex]a)\ A=\dfrac{3\times3\times3}{5\times5\times5\times5}[/tex]

[tex]A=\dfrac{3^3}{5^4}[/tex]

[tex]\boxed{A=3^3\times5^{-4}}[/tex]

[tex]b)\ B=\dfrac{16}{25\times49}\\\\[/tex]

[tex]B=\dfrac{4^2}{5^2\times7^2}[/tex]

[tex]\boxed{B=4^2\times5^{-2}\times7^{-2}}[/tex]

Exercice 6

[tex]a)\ 5^{-15}\times5^{-22}=5^{-15-22}\\\\\boxed{5^{-15}\times5^{-22}=5^{-37}}[/tex]

[tex]b)\ (-3)^{41}\times(-5)^{-41}=[(-3)\times(-5)]^{41}\\\\\boxed{(-3)^{41}\times(-5)^{-41}=15^{41}}[/tex]

[tex]c)\ 8^4\times8^{-14}=8^{4-14}\\\\\boxed{8^4\times8^{-14}=8^{-10}}[/tex]

[tex]d)\ \dfrac{3^{-40}}{3^{-12}}=3^{-40-(-12)}[/tex]

[tex]\dfrac{3^{-40}}{3^{-12}}=3^{-40+12}[/tex]

[tex]\boxed{\dfrac{3^{-40}}{3^{-12}}=3^{-28}}[/tex]

[tex]e)\ \boxed{\dfrac{5^8}{7^8}=(\dfrac{5}{7})^8}[/tex]

[tex]f)\ ((-5)^{-12})^5=(-5)^{-12\times5}\\\\((-5)^{-12})^5=(-5)^{-60}[/tex]

[tex]\boxed{((-5)^{-12})^5=5^{-60}}[/tex]

Exercice 7

[tex]a)\ (\dfrac{4}{5})^2=\dfrac{4^2}{5^2}\\\\\boxed{ (\dfrac{4}{5})^2=\dfrac{16}{25}}[/tex]

[tex]b)\ (\dfrac{-3}{2})^4=\dfrac{(-3)^4}{2^4}\\\\\boxed{(\dfrac{-3}{2})^4=\dfrac{81}{16}}[/tex]

[tex]c)\ (\dfrac{1}{3})^{-3}=\dfrac{1^{-3}}{3^{-3}}[/tex]

[tex](\dfrac{1}{3})^{-3}=\dfrac{1}{3^{-3}}[/tex]

[tex](\dfrac{1}{3})^{-3}=3^3[/tex]

[tex]\boxed{(\dfrac{1}{3})^{-3}=27}[/tex]