Как это решить? (с объяснением)

3 * (2/5)^2) + (50^5)/(20^6) : (25/4)^3 =

__ (2/5)^2 = 2^2 / 5^2
__ (50)^5 = (5^2 * 2)^5 = 5^10 * 2^5
__ (20^6) = (2^2 * 5)^6 = 2^12 * 5^6
__ (25/4) = ((5/2)^2)3 = 5^6 / 2^6
=>
= 3 * 2^2/5^2 + (5^10 * 2^5)/(5^6 * 2^12) : (5^6/2^6) =

= 3 * 2^2/5^2 + (5^10/5^6) * (2^5/2^12) : ((5^6 / 2^6) =

= 3 * 2^2/5^2 + (5^4 * 2^(-7)) * (2^6 / 5^6) =

= 3 * 2^2/5^2 + (5^4/5^6) * (2^(-7)* 2^6) =

= 3 * 2^2/5^2 + (5^(-2)) * (2^(-1)) =

= 3 * 2^2/5^2 + (1/5^2) * (1/2) =

= (3 * 2 * (2^2) + 1) / 5^2 =

= 25/25 = 1

50/20 в шестой - это 5/2 в 6й

Выполним операции по порядку:

(3(2/5)^2) + (50^5)/(20^6)/(25/4)^3 =

= (3 * 4/25) + (31250000000)/(20^6)/(625/64) =

= 12/25 + (31250000000)/(20^6 * 625/64) =

= 12/25 + (31250000000)/(5^6 * 2^6 * 625/64) =

= 12/25 + (31250000000)/(5^6 * 2^6 * 625/64) =

= 12/25 + (31250000000)/(5^6 * 2^6 * 625/64) =

= 12/25 + (31250000000)/(5^6 * 2^6 * 625/64) =

= 12/25 + (31250000000)/(5^6 * 2^6 * 625/64) =

= 12/25 + (31250000000)/(5^6 * 2^6 * 625/64) =

= 12/25 + (31250000000)/(5^6 * 2^6 * 625/64) =

= 12/25 + (31250000000)/(5^6 * 2^6 * 625/64) ≈

≈ 0,48 + 0,16 ≈

≈ 0,64

Ответ: примерно 0,64.

сперва убери степени, а потом раскрой скобки