Question

Scrieti sub forma de puteri care au aceeasi baza:
4 pe 9 la puterea 5 si 8 pe 27 la puterea 4
25 pe 36 la puterea 11 si 125 pe 216 la puterea 12

Answer 1

[tex]( \frac{4}{9}) ^{5}= \frac{2^{2} }{ 3^{2} }^{5} = \frac{2^{10} }{ 3^{10} } = (\frac{2}{3})^{10} \\ \\ (\frac{8}{27} ) ^{4}= (\frac{2^{3} }{3^{3} })^{4}= (\frac{2}{3})^{12} \\ \\ ( \frac{25}{36})^{11} = (\frac{5^{2} }{6^{2} } )^{11}= (\frac{5 }{6} )^{2*11}=(\frac{5 }{6} )^{22} \\ \\ ( \frac{125}{216})^{12} =( \frac{5^{3} }{6^{3} })^{12}=( \frac{5 }{6})^{36}[/tex]