a expressao [(0,5)2]3.[(1/16)3]4 e equivalente a qual potencia de base 2?
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Olá.
Temos a expressão:
![\mathsf{\left[\left(0,5\right)^2\right]^3\cdot\left[\left(\dfrac{1}{16}\right)^3\right]^4}](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Cleft%5B%5Cleft%280%2C5%5Cright%29%5E2%5Cright%5D%5E3%5Ccdot%5Cleft%5B%5Cleft%28%5Cdfrac%7B1%7D%7B16%7D%5Cright%29%5E3%5Cright%5D%5E4%7D "\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:
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}}}](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Cleft%5B%5Cleft%280%2C5%5Cright%29%5E2%5Cright%5D%5E3%5Ccdot%5Cleft%5B%5Cleft%28%5Cdfrac%7B1%7D%7B16%7D%5Cright%29%5E3%5Cright%5D%5E4%3D%7D%5C%5C%5C%5C%5C%5C+%5Cmathsf%7B%5Cleft%5B%5Cleft%28%5Cdfrac%7B1%7D%7B2%7D%5Cright%29%5E2%5Cright%5D%5E3%5Ccdot%5Cleft%5B%5Cleft%28%5Cdfrac%7B1%7D%7B2%5E4%7D%5Cright%29%5E3%5Cright%5D%5E4%3D%7D%5C%5C%5C%5C%5C%5C+%5Cmathsf%7B%5Cleft%5B%5Cleft%282%5E%7B-1%7D%5Cright%29%5E2%5Cright%5D%5E3%5Ccdot%5Cleft%5B%5Cleft%282%5E%7B-4%7D%5Cright%29%5E3%5Cright%5D%5E4%3D%7D%5C%5C%5C%5C%5C%5C+%5Cmathsf%7B%5Cleft%5B2%5E%7B-1%5Ccdot2%7D%5Cright%5D%5E3%5Ccdot%5Cleft%5B2%5E%7B-4%5Ccdot3%7D%5Cright%5D%5E4%3D%7D%5C%5C%5C%5C%5C%5C+%5Cmathsf%7B%5Cleft%5B2%5E%7B-2%7D%5Cright%5D%5E3%5Ccdot%5Cleft%5B2%5E%7B-12%7D%5Cright%5D%5E4%3D%7D%5C%5C%5C%5C%5C%5C+%5Cmathsf%7B2%5E%7B-2%5Ccdot3%7D%5Ccdot2%5E%7B-12%5Ccdot4%7D%3D%7D%5C%5C%5C%5C%5C%5C+%5Cmathsf%7B2%5E%7B-6%7D%5Ccdot2%5E%7B-48%7D%3D%7D%5C%5C%5C%5C%5C%5C+%5Cmathsf%7B2%5E%7B-6%2B%28-48%29%7D%3D%7D%5C%5C%5C%5C%5C%5C+%5Cmathsf%7B2%5E%7B-6-48%7D%3D%7D%5C%5C%5C%5C%5C%5C+%5Cboxed%7B%5Cmathsf%7B2%5E%7B-54%7D%7D%7D "\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.
Temos a expressão:
Usaremos as seguintes propriedades de potências:
Vamos aos cálculos.
Quaisquer dúvidas, deixe nos comentários.
Bons estudos.
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