Question

0,125¯1 *(5 корень4 * 5 корень 8) ¯2​

Answer 1

$0.125^{ - 1} \times (5 \sqrt{4} \times 5 \sqrt{8} )^{ - 2} = \\ = ( \frac{1}{8} )^{ - 1} \times (5 \times 2 \times 5 \sqrt{8} )^{ - 2} = \\ = 8 \times {5}^{ - 2} \times 2^{ - 2} {5}^{ -2} \times {8}^{ - 1} = \\ = {2}^{3} \times {5}^{ - 2} \times {2}^{ - 2} \times {5}^{ - 2} \times {2}^{ - 3} = \\ = 2^{ - 2} \times {5}^{ - 4}$

Answer 2

To simplify the expression, let's break it down step by step:

Step 1: Simplify the square roots. The square roots can be simplified as follows: √4 = 2 √8 = √(4 * 2) = √4 * √2 = 2√2

Step 2: Multiply the simplified square roots. 5√4 * 5√8 = 5 * 2 * 2√2 = 20√2

Step 3: Calculate the reciprocal and square of the expression. (20√2)^(-2) = 1 / (20√2)^2 = 1 / (400 * 2) = 1 / 800

Finally, the simplified expression is 1/800.