Question

a expressão 8^12 . 25^15 pode ser escrita na forma 2^x .10^y o valor de x+y é?​

Answer 1

$8^{12}~.~25^{15}\\\\\\\left(2^3\right)^{12}~.~\left(5^2\right)^{15}\\\\\\2^{\,3~.~12}~.~5^{\,2~.~15}\\\\\\2^{36}~.~5^{30}\\\\\\2^{16}~.~2^{30}~.~5^{30}\\\\\\2^{16}~.~\left(2^{30}~.~5^{30}\right)\\\\\\2^{16}~.~\left(2~.~5\right)^{30}\\\\\\\boxed{2^{16}~.~10^{30}}$

Os expoentes são x = 16 e y = 30, logo a soma "x+y" pedida vale 46.