Q.3 Say true or false and justify your answer: (i)\( 10 × 10^11 = 100^11\)
(ii) \( 2^3 > 5^2 \)
(iii)\( 2^3 × 3^2 = 6^5 \)
(iv) \( 3^20 = (1000)^0 \)


Answer :

(i)LHS = \( 10 × 10^11 = 10^{1+11} = 10^{12} \)
RHS\( = 100^11 = (10^2)^11 = 10^22 \)
\( 10^12 \neq 10^22 \)
\(\therefore \) Statement is false.
(ii)\( 2^3 > 5^2 \)
LHS = \(2^3 = 8 \)
RHS =\( 5^2 = 25 \)
8 < 25
\(\therefore 2^3 < 5^2 \)
Thus, the statement is false.
(iii) \(2^3 × 3^2 = 6^5 \)
LHS \(= 2^3 × 3^2 = 8 × 9 = 72 \)
RHS \(= 6^5 = 6 × 6 × 6 × 6 × 6 = 7776 \)
\( 72 \neq 7776 \)
\(\therefore \)The statement is false.
(iv)\( 3^0 = (1000)^0 \)
LHS = \( 3^0 = 1 \)
RHS = \( (1000)^0 = 1 \)
LHS = RHS

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