Question

Se a=10⁻¹ e b=10⁻² determine o valor da expressão a seguir. 

a.b⁻² . (a⁻¹.b²)⁴ . (a.b⁻¹)²
-------------------------------- 
a⁻³.b . (a².b⁻¹) . (a⁻¹.b)

Answer 1

$\frac{a.b^{-2}.(a^{-1}.b^{2}).(a.b^{-1})^{2}}{a^{-3}.b.(a^{2}.b^{-1}).(a^{-1}.b)}$

$\frac{10^{-1}.(10^{-2})^{2}.[(10^{-1})^{-1}.(10^{-2})^{2}]^{4}.[(10^{-1}).(10^{-2})^{-1}]^{2}}{(10^{-1})^{-3}.10^{-2}.[(10^{-1})^{2}.(10^{-2})^{-1}].[(10^{-1})^{-1}.10^{-2}]}$

$\frac{10^{-1}.10^{+4}.[(10^{+1}).(10^{-4})]^{4}.[(10^{-1}.10^{2})]^{2}}{10^{3}.10^{-2}.(10^{-2}.10^{2}).(10^{1}.10^{-2})}$

$\frac{10^{-3}.[10^{-3}]^{4}.[10^{1}]^{2}}{10^{1}.10^{0}.10^{-1}}$

$\frac{10^{-3}.10^{-12}.10^{2}}{10^{1+0+(-1)}}$

$\frac{10^{-3+(-12)+2}}{10^{0}}$

$\frac{10^{-13}}{1}$ ou $10^{-13}$

Quando for potencia de potencia você multiplica as potências, quando for multiplicação e as bases forem as mesmas você conservas as bases e somas os expoentes.