Question

Here is a simple question Answer it

Simplify and give answer.

${2}^{ - 1} \times {4}^{ - 1} = {2}^{ - 2}$
Answer only if u know .​

Answer 1

Appropriate Question :-

Simplify and give the answer ;

${ \sf { \bigg ( {2}^{ - 1} × {4}^{ - 1} } \bigg ) + {2}^{ - 2} }$

Solution :-

We all are well aware of a identity i.e :-

${ \boxed { \bf { \sf { \underline { {a}^{- b} = \dfrac{1}{{a}^{b}} } } } } }$

So we are going to use this identity in the given Question ;

${ \sf { \bigg ( {2}^{ - 1} × {4}^{ - 1} } \bigg ) + {2}^{ - 2} }$

${ : \Rightarrow { \sf { \bigg ( {\dfrac{1}{2¹} × \dfrac{1}{4¹} } \bigg ) + \dfrac{1}{2²} } } }$

${ : \Rightarrow { \sf { \bigg ( {\dfrac{1}{2} × \dfrac{1}{4} } \bigg ) + \dfrac{1}{4} } } }$

${ : \Rightarrow { \sf { \dfrac{1}{8} + \dfrac{1}{4} } } }$

${ : \Rightarrow { \sf { \dfrac{ 1 + 2 }{8} } } }$

${ \boxed { \underline { \bf { \sf { \dfrac{3}{8} } } } } }$

Henceforth , The Required Answer is ⅜