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

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## Question

(i) $$10 × 10^{11} = 100^{11}$$

(ii) $$2^3 > 5^2$$

(iii) $$2^3 × 3^2 = 6^5$$

(iv) $$3^0 = 1000^0$$

Video Solution
Exponents And Powers
Ex 13.2 | Question 3

## 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}

$$LHS \rm\!=\!2^3\!\times\!3^2\!=\!2 \!\times\!2\!\times\!2\!\times\!3\!\times\!3\!=\!72$$

$$RHS \rm\!=\! 6^5\!=6\!\times\!6\!\times\!6\!\times\!6\!\times\!6\!=\!7776$$

$$\therefore 2^3 \times 3^2\ne 6^5$$

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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