Gujarat BoardEnglish MediumSTD 7MATHSExponents and Powers2 Marks
Question
Say true or false and justify your answer: $10 \times 10^{11} = 100^{11}$
✓
Answer
By the law of exponents we have,
$x^m \times x^n=x^{m+n}$
$\text { L.H.S. }=1010^{11}=10^{1 \times 10^{11}}$
$=10^{1+11}=10^{12}$
Hence $10 \times 10^{11}=10^{12}$
And
$100^{11}=(10 \times 10)^{11}=\left(10^2\right)^{11}$
$=10^{22}=\text { R.H.S. }$
Since $10^{12} \neq 10^{22}$
So, $10 \times 10^{11} \neq 100^{11}$
$\therefore 10 \times 10^{11}=100^{11}$ is False.
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