Question

Say true or false and justify your answer:$10\times {10}^{11}={100}^{11}$

• A. True
• B. False

Answer 1

The correct option is B False

Step 1: Solving LHS

Let us solve the given exponential equation by considering Left Hand Side (LHS) and Right-Hand Side (RHS)

The Left-Hand Side (LHS)=$10\times {10}^{11}={100}^{11}$

$$\begin{gathered} ={10}^{1+11}\left[\because a^m\times a^n=a^{m+n}\right] \\ ={10}^{12} \end{gathered}$$

Step 2: Solving RHS

The Right-Hand Side (RHS)=${100}^{11}$

$$\begin{gathered} ={100}^{11}={(10\times 10)}^{11} \\ ={\left({10}^{1+1}\right)}^{11} \\ ={\left({10}^2\right)}^{11} \\ ={\left(10\right)}^{2\times 11}\sin ce\left[\because {\left(a^m\right)}^n=a^{mn}\right] \\ ={10}^{22} \end{gathered}$$

On comparing LHS & RHS, we get;

LHS ≠ RHS

Hence, the given statement is false.