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

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(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.


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

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