Question

alguém mim ajuda por ​ favor!!!​

Answer 1

Resposta:

$11~~divisao~de~potencias~de~mesma~base\\ \\mantenha~a~base~e~subtraia~os~expoentes\\\\multiplicacao~de~potencias~de~mesma~base\\ \\mantenha~a~base~e~some~os~expoentes \\ \\ a)~~2^{x} .2^{5} =2^{(x+5)}\\ \\ b)~~7^{x} :7^{7} =7^{(x-7)} \\ \\ c)~~(8^{x})^{4} =8^{4x} \\ \\ d)~~2^{5x}. 2^{-3x} =2^{5x+(-3x)}=2^{(5x-3x)} =2^{2x} \\ \\ e)~~9^{2x}: 9^{-2x} =9^{2x-(-2x)} =9^{2x+2x} =9^{4x} \\ \\ f)~~7^{x}.7^{(x+8)} =7^{x+x+8} =7^{2x+8} \\ \\ g)~~3^{x+2}.3^{x-2} =3x^{x+2+x-2} =3^{2x}$

$h)~~3^{x}: 3^{-2}=3^{x-(-2)} =3^{(x+2)} \\ \\ 12\\ \\ a^{3}-2a^{3} x^{3} y^{3} ~~para~x=-3,~a=10,~y=-1\\ \\ 10^{3} -2.10^{3} .(-3)^{3} .(-1)^{3} =1000-2000.(-27).(-1)=\\ \\ 1000+54000=55000$

$13\\ \\ 3x=(-9)^{2}~~~~~~x=\frac{(-9)^{2} }{3}~~~~~~ x=\frac{81}{3} ~~~~~~x=27\\ \\ 5y=(-5)^{3} ~~~~~~y=\frac{(-5)^{3} }{5} ~~~~~~y=-\frac{125}{5} ~~~~~~y=25\\ \\ x^{2} +y^{2} =27^{2}+25^{2} =729+625=1354$

$14\\ \\ (0,3)^{2} +(0,15)^{2} =0,09+0,0225=0,1125\\ \\ 15\\ \\ \left[\begin{array}{ccc}5^{3 } +(8-5)^{2} \end{array}\right] .(12-8)^{3} =\\ \\ (5^{3}+3^{2}) .4^{3} =(125+9).64=134~.~64=8576$