Question

Evaluate [ { ( 2^-1 )^-1 }^-1 ]^-1​

Answer 1

♣ Qᴜᴇꜱᴛɪᴏɴ :

$\large\boxed{\sf{Evaluate\:\:\left[\:\:\left\{\left(\:2^{-1}\:\right)^{-1}\right\}^{-1}\:\right]^{-1}}}$

♣ ᴀɴꜱᴡᴇʀ :

$\large\boxed{\sf{\:\left[\:\:\left\{\left(\:2^{-1}\:\right)^{-1}\right\}^{-1}\:\right]^{-1}=2}}$

♣ ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴꜱ :

$\sf{\left(2^{-1}\right)^{-1}: 2}$

$=\left(\left\{2\right\}^{-1}\right)^{-1}$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^{-1}=\dfrac{1}{a}$

$=\dfrac{1}{2^{-1}}$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^{-1}=\dfrac{1}{a}$

$2^{-1}=\dfrac{1}{2}$

$=\dfrac{1}{\dfrac{1}{2}}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \dfrac{1}{\dfrac{b}{c}}=\dfrac{c}{b}$

$=\dfrac{2}{1}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \dfrac{a}{1}=a$

$\huge\boxed{\sf{=2}}$