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Exponents and Powers — MATHS STD 7 — Question

Gujarat BoardEnglish MediumSTD 7MATHSExponents and Powers1 Mark
Question
Say true or false and Justify your answer.
$10 \times 10^{11}=100^{11}$
✓

Answer

False, $10 \times 10^{11} \neq 100^{11}$
Justification
LHS $=10 \times 10^{11}=10^{1+11}=10^{12} \quad\left[\because a^m \times a^n=a^{m+n}\right]$
RHS $=(100)^{11}=\left(10^2\right)^{11} \quad\left[\because 100=10 \times 10=10^2\right]$
$=10^{2 \times 11}=10^{22} \quad\left[\because\left(a^m\right)^n=a^{m n}\right]$
$\because \quad 10^{12} \neq 10^{22}$, so LHS $\neq$ RHS
Therefore, $10 \times 10^{11} \neq 100^{11}$

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