Question

порівняти 2^100 і 16^25, 2^300 і 3^200

Answer 1

Ответ:

$2^{100}=16^{25} \ ; \ 2^{300}$

Объяснение:

$16^{25}=(2^{4})^{25}=2^{4 \cdot 25}=2^{100} \Rightarrow 2^{100}=16^{25};$

$2^{300}=2^{3 \cdot 100}=(2^{3})^{100}=8^{100}; \ 3^{200}=3^{2 \cdot 100}=(3^{2})^{100}=9^{100};$

$8$

Answer 2

To compare these expressions, let's calculate the values for each and then compare them:

1. Comparing $2^{100}$ and $16^{25}$:

   • $2^{100}$ can be calculated as $1.2676506 \times 10^{30}$ (approximately).
   • $16^{25}$ can be calculated as $1.2089258 \times 10^{31}$ (approximately).

   Therefore, $16^{25}$ is larger than $2^{100}$.

2. Comparing $2^{300}$ and $3^{200}$:

   • $2^{300}$ can be calculated as $1.0715086 \times 10^{90}$ (approximately).
   • $3^{200}$ can be calculated as $3.6561584 \times 10^{95}$ (approximately).

   Therefore, $3^{200}$ is larger than $2^{300}$.

In both cases, the exponentiation involving 3 is larger than the one involving 2.