Ex 13.1 Q4 Exponents and Powers Solution - NCERT Maths Class 7

Go back to  'Ex.13.1'

Question

 Identify the greater number, wherever possible, in each of the following?

(i) \({{4}^{3}}\text{ or }{{3}^{4}}\,\)     (ii) \({{5}^{3}}\text{ or }{{3}^{5}}\)     (iii) \({{2}^{8}}\text{ or }{{8}^{2}}\)

(iv) \({{100}^{2}}\text{ or }{{2}^{100}}\)     (v)  \({{2}^{10}}\text{ or }{{10}^{2}}\)

Text Solution

What is known? 

Exponential form

Reasoning:

In this question exponential form of the number is given. That means we know the base and exponent. We will solve by multiplying the given base to the number of times of its exponent and then compare the two number to find which is greater.

(i) \(4^3\) or \( 3^4\)

\(3\) times \(4\) \(=\) \( 4 \times 4 \times 4 =64 \)

\(4\) times \(3\) \(=\) \(\rm 3\times3\times3\times3 =81\)

Since \(81 \gt 64\)

So, \(3^4\) is greater than \(4^3\)

(ii) \(5^3\) or \(3^5\)

\(3\) times \(5\) \(=\) \(\rm 5\times5\times5=125\)

\(5\) times \(3\) \(=\) \(\rm 3\times3\times3\times3\times3=243\)

Since \(243 \gt 125\)

So, \(3^5\) is greater than \(5^3\)

(iii) \(2^8\) or \(8^2\)

\(8\) times \(2\) \(=\) \(\rm 8\times8=256\)  

\(2\) times \(8\) \(=\) \(\rm 2\times2\times2\times2\times2\times2\times2\times2=64\)

Since \(256 \gt 64\)

So, \(2^8\) is greater than \(8^2\)

(iv) \(100^2\) or \(2\)\(100\)

\(2\) times \(100\) \(=\) \(\rm 100 \times 100 =10,000\)

\(100 \) times \(\rm 2 = 2\times2\times2\times2\times2\times........\times100 \) times \(= 16,384\)

Since \(16,384 > 10,000\)

So, \(100^2\) is greater than \(2^{100}\)

(v) \(2 \)\( 10\) or \(10^2\) 

\(10\) times \(2\) \(=\) \(1024\)

\(2\) times \(10\) \(=\) \(100\)

Since \(1024 > 100\)

So, \(2\)\(10\) is greater than \(10^2\)