Question

a expressao [(0,5)2]3.[(1/16)3]4 e equivalente a qual potencia de base 2?

Answer 1

Olá.

Temos a expressão:

$\mathsf{\left[\left(0,5\right)^2\right]^3\cdot\left[\left(\dfrac{1}{16}\right)^3\right]^4}$

Usaremos as seguintes propriedades de potências:

$\mathsf{\dfrac{1}{a^n}=a^{-n}}\\\\\mathsf{(a^r)^s=a^{r\cdot s}}\\\\ \mathsf{a^m\cdot a^n=a^{m+n}}$
Vamos aos cálculos.

$\mathsf{\left[\left(0,5\right)^2\right]^3\cdot\left[\left(\dfrac{1}{16}\right)^3\right]^4=}\\\\\\ \mathsf{\left[\left(\dfrac{1}{2}\right)^2\right]^3\cdot\left[\left(\dfrac{1}{2^4}\right)^3\right]^4=}\\\\\\ \mathsf{\left[\left(2^{-1}\right)^2\right]^3\cdot\left[\left(2^{-4}\right)^3\right]^4=}\\\\\\ \mathsf{\left[2^{-1\cdot2}\right]^3\cdot\left[2^{-4\cdot3}\right]^4=}\\\\\\ \mathsf{\left[2^{-2}\right]^3\cdot\left[2^{-12}\right]^4=}\\\\\\ \mathsf{2^{-2\cdot3}\cdot2^{-12\cdot4}=}\\\\\\ \mathsf{2^{-6}\cdot2^{-48}=}\\\\\\ \mathsf{2^{-6+(-48)}=}\\\\\\ \mathsf{2^{-6-48}=}\\\\\\ \boxed{\mathsf{2^{-54}}}$

Quaisquer dúvidas, deixe nos comentários.
Bons estudos.