Question

10×10"=100"true/false​

Answer 1

${ \underline {\underline{ \sf \purple{Correct\:Question}}}}$

$\begin{gathered}\frak{ \pink{True \: or \: False }} \begin{cases} & \sf{} \\ & \sf{10 \times 10 {}^{11} = 100 {}^{11} } \\ & \sf{} \end{cases}\\ \\\end{gathered}$

${ \underline {\underline{ \sf \purple{Formula}}}}$

$\bigstar \rm \: a {}^{m} \times a {}^{n} = a {}^{m + n} \\ \\\bigstar \rm \: (a {}^{m} ) {}^{n} = a {}^{m \times n} \quad$

${ \underline {\underline{ \sf \purple{Solution}}}}$

$\rm \: \leadsto \bigstar Solving \: LHS$

$\rm\longmapsto \: 10 \times 10 {}^{11}$

$\rm\longmapsto \: 10 {}^{1} \times 10 {}^{11}$

$\rm \bigstar Applying \: the \: Formula \: \hookrightarrow \: \rm \: a {}^{m} \times a {}^{n} = a {}^{m + n}$

$\rm\longmapsto \: 10 {}^{1 + 11}$

$\rm\longmapsto \: 10 {}^{12}$

$\leadsto \bigstar \rm Solving \: RHS$

$\rm\longmapsto \: 100{}^{11}$

$\rm\longmapsto \: (10 \times 10 ){}^{11}$

$\rm\longmapsto \: (10 {}^{2} ){}^{11}$

$\rm \bigstar Applying \: the \: Formula \: \hookrightarrow \:\rm \: (a {}^{m} ) {}^{n} = a {}^{m \times n}$

$\rm\longmapsto \: 10 \: {}^{2 \times 11}$

$\rm\longmapsto \: 10 \: {}^{22}$

$\rm \therefore \green{ LHS} \: is \: not \: equal \: to \: \red{ RHS}$

$\rm Hence, it \: is \: \blue{ False}$

${ \underline {\underline{ \sf \purple{Required \: Answer}}}}$

$\bigstar \leadsto\boxed{ \bf False}$

$\bigstar \mathtt {@iTzShInNY} \bigstar$