Ex.13.2 Q3 Exponents and Powers Solutions - NCERT Maths Class 7

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Question

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) \(3^0 = 1000^0\)

Text Solution

Steps:

(i) \(\begin{align}10\,\,\times \,{{10}^{11}}={{100}^{11}} \end{align}\)

\(LHS\) \(= 10 \times 10 ^{11} = 10^{11+1}=10^{12}\)

\(RHS\) \(=\) \(100^{11}=(10^2)^{11}=10^{22}\)

\(\therefore 10^{12} \ne 10^{22}\)

\(\therefore\)Thus,the statement is false.

(ii) \(\begin{align}{{2}^{3}}>\text{ }{{5}^{2}}\end{align}\)

\(LHS \rm= 2^3=2 \times2\times2=8 \)

\(RHS \rm = 5^2=5\times5=25 \)

\(\therefore 2^3<5^2\)

Thus,the statement is false.

(iii) \(\begin{align}{{2}^{5}}\rm x\text{ }{{3}^{5}}=\text{ }{{6}^{5}}\end{align}\)

\(LHS \rm= 2^3\times3^2=2 \times2\times2\times3\times3=72 \)

\(RHS \rm = 6^5=6\times6\times6\times6\times6=7776 \)

\(\therefore 2^3 \times 3^2\ne 6^5\)

Thus,the statement is false.

(IV) \(\begin{align}\,{3^0} = {\rm{ }}{1000^0} = {\rm{ }}1\end{align}\)

Thus ,the statement is true.

  
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