Question

which is greater 100 to the power 3 or 3 to the power 100​

Answer 1

Answer:

$3 {}^{100}$

is greater than

$100 {}^{3}$

Answer 2

Answer:

$3^{100}$ > $100^3$

Step-by-step explanation:

$100^3$

$=10^{2^3}$

$=10^6$ [∵ $a^{m^n} = a^{mn}$]

$3^{100}$

$=3^{(10).(10)}$

$=3^{(10)^{(10)}}$ [∵ $a^{m^n} = a^{mn}$]

$=3^{(3 + 7)^{(10)}}$

$=(3^3.3^7)^{(10)}}$ [∵ $a^{m+n} = (a^m).(a^n)$]

$=(27.3^7)^{(10)}}$

Now 27> 10

∴ $(27.3^7)$ > 10

And 10> 6

∴ $(27.3^7)^{(10)}}$ > $10^6$

∴ $3^{100}$ > $100^3$