Question

Resolva a expressão

(1/4)-¹ . (1/2)² + 4².4-³

Answer 1

Olá.

Nessa questão aplicaremos algumas propriedades de potências, que demonstro abaixo.

$\diamondsuit~\Large\boxed{\boxed{\mathsf{r^{-s}=\dfrac{1}{r^s}~\therefore~\dfrac{1}{r}^{-s}=r^s}}}$

$\diamondsuit~\Large\boxed{\boxed{\mathsf{\left(\dfrac{x}{y}\right)^z=\dfrac{x^z}{y^z}}}}$

$\diamondsuit~\Large\boxed{\boxed{\mathsf{a^r\cdot a^s=a^{r+s}}}}$

Vamos aos cálculos.

$\Large\begin{array}{l} \mathsf{\left(\dfrac{1}{4}\right)^{-1}\cdot\left(\dfrac{1}{2}\right)^{2}+4^2\cdot4^{-3}=}\\\\\\ \mathsf{\left(4^1\right)\cdot\left(\dfrac{1^{2}}{2^2}\right)+4^2\cdot4^{-3}=}\\\\\\ \mathsf{4^1\cdot\left(\dfrac{1}{4}\right)+4^2\cdot4^{-3}=}\\\\\\ \mathsf{4^1\cdot4^{-1}+4^2\cdot4^{-3}=}\\\\ \mathsf{4^{1-1}+4^{2-3}}=}\\\\ \mathsf{4^{0}+4^{-1}}=}\\\\ \mathsf{1+\dfrac{1}{4}}=}\\\\ \mathsf{\dfrac{4\cdot1+1}{4}=}\boxed{\mathsf{\dfrac{5}{4}}}} \end{array}$

Quaisquer dúvidas, deixe nos comentários.
Bons estudos.

Answer 2

Oie, Td Bom?!

$= ( \frac{1}{4} ) {}^{ - 1} \: . \: ( \frac{1}{2} ) {}^{2} + 4 {}^{2} \: . \: 4 {}^{ - 3}$

$= ( \frac{1}{2 {}^{2} } ) {}^{ - 1} \: . \: ( \frac{1}{2} ) {}^{2} + 4 {}^{2 - 3}$

$= ( 2 {}^{ - 2} ) {}^{ - 1} \: . \: ( \frac{1}{2} ) {}^{2} + 4 {}^{ - 1}$

$= 2 {}^{2} \: . \: ( \frac{1}{2} ) {}^{2} + 4 {}^{ - 1}$

$= (2 \: . \: \frac{1}{2} ) {}^{2} + (2 {}^{2} ) {}^{ - 1}$

$= (2 \: . \: \frac{1}{2} ) {}^{2} + 2 {}^{ - 2}$

$= 1 {}^{2} + \frac{1}{2 {}^{2} }$

$= 1 + \frac{1}{4}$

$= \frac{4 + 1}{4}$

$= \frac{5}{4}$

Att. Makaveli1996