Question

please tell me this one am in class 7 this chapter is in maths exponents and powers..​ take out the values of 100²..​

Answer 1

Working out:

We are given with two exponents with their bases in the attachment, and we have to compare them.

• $\sf{{100}^{2} \: or \: {2}^{100} }$

Here, the exponents and the bases are different. So, let's first convert them into same exponents. 2 is smaller than 100, So let's make the exponents in 2s.

$\sf{ \longrightarrow{ {2}^{100} }}$

$\sf{ \longrightarrow{ {2}^{50 \times 2} }}$

$\sf{ \longrightarrow{( {2}^{50} ) {}^{2} }}$

Now we can compare 100² and (2⁵⁰)² because the screen exponent is now same i.e 2.

By looking at the exponent table and sequence of 2, we know that 2⁷ = 128 which exceeds 100. And of course, 2⁵⁰ > 2⁷ (2⁵⁰ is far greater than 2⁷).

So,

$\sf{ \longrightarrow{ {2}^{50} > {2}^{7} }}$

$\sf{ \longrightarrow{ ({2}^{50}) > 100 }}$

$\sf{ \longrightarrow{( {2}^{50) {}^{2} } > {100}^{2} }}$

$\sf{ \longrightarrow{ \red{ {2}^{100} > {100}^{2} }}}$

So, we can say that 2¹⁰⁰ is greater than 100². And we are done comparing these exponents !!