Ex 13.1 Q6 Exponents and Powers Solution- NCERT Maths Class 7

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Question

 Simplify:

(i)  \(2\times {{10}^{3}}\)   

(ii) \({{7}^{2}}\times {{2}^{2}}\)   

(iii) \({{2}^{3}}\times 5\)     

(iv) \(3\times {{4}^{4}}\)

(v) \(0\times {{10}^{2}}\)   

(vi) \({{5}^{2}}\times {{3}^{3}}\)   

(vii) \({{2}^{4}}\times {{3}^{2}}\)   

(viii)  \({{3}^{2}}\times {{10}^{4}}\)

Text Solution

What is known?

Base and exponent.

What is unknown?

Simple form of the number.

Reasoning:.

In this question we will multiply the base and the number of times it’s exponent to simplify the given statement.

(i)

\[\begin{align} 2\times {{10}^{3}}&=2\times (10\times 10\times 10)\\&=2\times 1000\\&=2000\end{align}\]

(ii)

\[\begin{align} {{7}^{2}}\times {{2}^{2}}&=(7\times 7)\times (2\times 2)\\&=49\times 4\\&=196\end{align}\]

(iii)

\[\begin{align}{{2}^{3}}\times 5&=(2\times 2\times 2)\times 5\\&=8\times 5\\&=40\end{align}\]

(iv)

\[\begin{align}3\times {{4}^{4}}&=3\times (4\times 4\times 4\times 4)\\&=3\times 256\\&=768\end{align}\]

(v)

\[\begin{align}0\times {{10}^{2}}&=0\times 10\times 10\\&=0\end{align}\]

(vi)

\[\begin{align}{{5}^{2}}\times {{3}^{3}}&=(5\times 5)\times (3\times 3\times 3)\\&=25\times 27\\&=675\end{align}\]

(vii)

\[\begin{align}{{2}^{4}}\!\times \!{{3}^{2}}&=(\!2\times\!\! 2\times \!2\times\!2)\!\times \!(3\!\times\!3)\\&=16\!\times\! 9\\&=144\end{align}\]

(viii) 

\[\begin{align}{3^2}\!\! \times\!\! {10^4}&=\!\! (3\!\!\times\!\!3)\!\!\times\!\!(10\!\!\times\!\!10\!\!\times\!\!10\!\!\times\!\!10) \\&= 9\!\times\!10000 \\&= 90000\end{align}\]

 

  
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