Question

1:8×1:6¯²×1:12³×40×1:6³×1:12¯⁴

Answer 1

Ответ смотри на фото.

Answer 2

To solve the expression 1:8×1:6¯²×1:12³×40×1:6³×1:12¯⁴, we need to first understand the notation used here.

In the notation "1:a", the colon (:) represents a ratio, and "a" represents the denominator of the ratio. The notation "a¯n" represents "a to the power of n". So, "1:a¯n" means "1 divided by a to the power of n".

Let's break down the expression step by step:

1. 1:6¯² means 1 divided by 6 squared: 1:6¯² = 1/(6²) = 1/36

2. 1:12³ means 1 divided by 12 cubed: 1:12³ = 1/(12³) = 1/1728

3. 1:6³ means 1 divided by 6 cubed: 1:6³ = 1/(6³) = 1/216

4. 1:12¯⁴ means 1 divided by 12 to the power of 4: 1:12¯⁴ = 1/(12⁴) = 1/20736

Now, let's combine the results:

1:8 × 1:6¯² × 1:12³ × 40 × 1:6³ × 1:12¯⁴

= 1/8 × 1/36 × 1/1728 × 40 × 1/216 × 1/20736

Now, let's simplify the expression:

= (1/8) * (1/36) * (1/1728) * (40) * (1/216) * (1/20736)

To simplify the multiplication, multiply all the numerators together and all the denominators together:

= 40 / (8 * 36 * 1728 * 216 * 20736)

Now, calculate the denominator:

8 * 36 * 1728 * 216 * 20736 = 219,902,325,555,968

Finally, divide 40 by the denominator:

= 40 / 219,902,325,555,968

The result is an extremely small decimal value, but to maintain precision, you can express it in scientific notation as:

≈ 1.8189894 × 10^(-16)