Question

Степени 3^123 больше или 9^99

Answer 1

Ответ:

3¹²³ меньше чем 9⁹⁹

Пошаговое объяснение:

9⁹⁹=(3³)⁹⁹=3²⁹⁷

Answer 2

To compare the values of 3^123 and 9^99, we can simplify both expressions and then make the comparison.

Let's start with 3^123:

3^123 = 3^(3*41) = (3^3)^41 = 27^41

Next, let's simplify 9^99:

9^99 = (3^2)^99 = 3^(2*99) = 3^198

Now we have both expressions in terms of powers of 3.

So the comparison is now between 27^41 and 3^198.

To compare them, we can divide both exponents by the greatest common divisor (GCD) of the exponents, which is 41:

27^41 / 3^41 and 3^198 / 3^41

Now we can compare the remaining expressions:

27^41 / 3^41 = (3^3)^41 / 3^41 = 3^(341) / 3^41 = 3^(341 - 41) = 3^82

And

3^198 / 3^41 = 3^(198-41) = 3^157

Now we have 3^82 and 3^157 to compare.

Since 157 > 82, we can conclude that 3^157 is greater than 3^82.

Thus, 3^123 (which is equal to 27^41) is less than 3^157, and therefore, 3^123 is less than 9^99.