Exponents numbers

• May 13th 2010, 01:20 PM
sri340
Exponents numbers
if 2^5 = 32 then 2^100 is close to

a 10^10 b 10^15 c 10^10 d 10^25 e 10^30
• May 13th 2010, 07:20 PM
Soroban
Hello, sri340!

Quote:

If $2^5 = 32$, then $2^{100}$ is close to:

$(a)\;10^{10} \qquad(b)\;10^{15} \qquad(c)\;10^{10} \qquad(d)\;10^{25} \qquad(e)\;10^{30}$

Given: . $2^5 \:=\:32$

Square: . $\left(2^5\right)^2 \:=\:32^2 \quad\Rightarrow\quad 2^{10} \:=\:1024$

. . . . . . . $2^{10} \;\approx\;1000 \quad\Rightarrow\quad 2^{10} \;\approx\;10^3$

Raise to the 10th power: . $\left(2^{10}\right)^{10} \:\approx\:\left(10^3\right)^{10}$

Therefore: . $2^{100} \;\approx\;10^{30}$ . . . answer (e)