Question

( ( 0,2)³) ⁻⁵ : 0,2 ⁻¹³

Answer 1

$(0,2 ^{3}) ^{-5}:0,2 ^{-13} \\ 0,2 ^{-15}:0,2 ^{-13} \\ 0,2 ^{-2}.$
Преобразуем десятичную дробь в обыкновенную:
$( \frac{1}{5}) ^{-2}. \\ \\ 5 ^{2}=25.$

Answer 2

Let's break down the expression step by step:

1. (0.2)³: This means raising 0.2 to the power of 3. (0.2)³ = 0.2 * 0.2 * 0.2 = 0.008

2. (0.008)⁻⁵: This means taking the reciprocal of 0.008 and then raising it to the power of 5. (0.008)⁻⁵ = 1 / (0.008)⁵ = 1 / (0.008 * 0.008 * 0.008 * 0.008 * 0.008) = 1 / 3.2768e-11 ≈ 3.05564651e+10

3. 0.2⁻¹³: This means taking the reciprocal of 0.2 and then raising it to the power of 13. 0.2⁻¹³ = 1 / 0.2¹³ = 1 / (0.2 * 0.2 * 0.2 * ... * 0.2) (13 times) = 1 / 1.5943239e-14 ≈ 6.26641625e+13

Now, let's divide the results from step 2 by step 3:

(3.05564651e+10) / (6.26641625e+13) ≈ 4.88018041e-4

So, the final result is approximately 4.88018041e-4.