Question

(50 PONTOS)

Reduza a uma só potência a seguinte expressão.

$\dfrac{(0,2)^{21}}{(5^{-1})^{-15}}$

Answer 1

Olá Expertiee.


Propriedades fracionária e de potenciação usada:

$\star ~\boxed{\boxed{\mathsf{a^{-k} \Leftrightarrow\dfrac{1}{a^k}}}}\\\\\\\\\star~\boxed{\boxed{\mathsf{\dfrac{a^k}{a^y}\Leftrightarrow a^{k-y}}}}$


Organizando e simplificando a fração:

$\mathsf{\dfrac{(0,2)^{21}}{(5^{-1})^{-15}}}\\\\\\\mathsf{\dfrac{\Big(\dfrac{2}{10}\Big)^{21}}{5^{-1\cdot -15}}}\\\\\\\mathsf{\dfrac{\Big(\dfrac{1}{5}\Big)^{21}}{5^{15}}}\\\\\\\mathsf{\dfrac{(5^{-1})^{21}}{5^{15}}}\\\\\\\mathsf{\dfrac{5^{-1\cdot 21}}{5^{15}}}\\\\\\\mathsf{\dfrac{5^{-21}}{5^{15}}}\\\\\\\mathsf{5^{-21-(15)}}\\\\\\\boxed{\mathsf{5^{-36}}}$


Dúvidas? comente.

Answer 2

.
$\frac{(0,2)^{21}}{(5^{-1})^{-15}} = \\ \\ ( \frac{2}{10} )^{21}\div5^{15}= \\ \\ ( \frac{1}{5} )^{21}\div5^{15}= \\ \\ 5^{-21}\div5^{15}= \\ \\ 5^{-21-15}= \\ \\ 5^{-36}$