Question

O valor expressão [10²¹. (10³)-³. (10² ).[(10¹)¹] / [(10²)²)-³] é:

Answer 1

O valor da expressão é  $10^{27}$.

Para melhor entender esta resolução, comecemos por relembrar algumas regras da potenciação:

• $a^m\times b^m=(a\times b)^m$

• $a^m\times a^n=a^{m+n}$

• $\dfrac{a^m}{a^n}=a^{m-n}$

• $\dfrac{a^m}{b^m}=\left(\dfrac{a}{b}\right)^{m}$

• $\left(a^m\right)^n=a^{m\times n}$

Com isto em mente, passemos à resolução do exercício.

    $\dfrac{10^{21}\times\left(10^{3}\right)^{-3}\times10^{2}\times\left(10^{1}\right)^1}{\left(\left(10^{2}\right)^2\right)^{-3}}=$

$=\dfrac{10^{21}\times10^{3\times(-3)}\times10^{2}\times10^{1\times1}}{\left(10^{2\times2}\right)^{-3}}=$

$=\dfrac{10^{21}\times10^{-9}\times10^{2}\times10^{1}}{\left(10^{4}\right)^{-3}}=$

$=\dfrac{10^{21}\times10^{-9}\times10^{2}\times10^{1}}{10^{4\times(-3)}}=$

$=\dfrac{10^{21}\times10^{-9}\times10^{2}\times10^{1}}{10^{-12}}=$

$=\dfrac{10^{21+(-9)}\times10^{2}\times10^{1}}{10^{-12}}=$

$=\dfrac{10^{21-9}\times10^{2}\times10^{1}}{10^{-12}}=$

$=\dfrac{10^{12}\times10^{2}\times10^{1}}{10^{-12}}=$

$=\dfrac{10^{12+2}\times10^{1}}{10^{-12}}=$

$=\dfrac{10^{14}\times10^{1}}{10^{-12}}=$

$=\dfrac{10^{14+1}}{10^{-12}}=$

$=\dfrac{10^{15}}{10^{-12}}=$

$=10^{15-(-12)}=$

$=10^{15+12}=$

$=10^{27}$

Podes ver mais exercícios de aritmética em:

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