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) \(2\times {{10}^{3}}=2\times (10\times 10\times 10)=2\times 1000=2000\)

(ii) \({{7}^{2}}\times {{2}^{2}}=(7\times 7)\times (2\times 2)=49\times 4=196\)

(iii) \({{2}^{3}}\times 5=(2\times 2\times 2)\times 5=8\times 5=40\)

(iv) \(3\times {{4}^{4}}=3\times (4\times 4\times 4\times 4)=3\times 256=768\)

(v) \(0\times {{10}^{2}}=0\times 10\times 10=0\)

(vi) \({{5}^{2}}\times {{3}^{3}}=(5\times 5)\times (3\times 3\times 3)=25\times 27=675\)

(vii) \({{2}^{4}}\times {{3}^{2}}=(2\times 2\times 2\times 2)\times (3\times 3)=16\times 9=144\)

\(\begin{align}\rm{(viii)}\,\,{3^2} \times {10^4} = (3 \times 3) \times (10 \times 10 \times 10 \times 10) = 9 \times 10000 = 90000\end{align}\)