Question

http://zadane.pl/zadanie/1354812

Błagam! POMÓŻCIE!

zad. 3 i 5!

Answer 1

5a)
(27 * 32) / (9*4)^2 =
(3^3 * 2^5) / (3^2^2 * 2^2^2) =
(3^3 * 2^5) / 3^4 * 2^4 =
3^(3-4) * 2^(5-4) =
3^(-1) * 2^1 =
2/3

5b)
5*900 / 3^4 * 25^2 =
5^1 * 3^2 * 4 * 5^2  /  3^4 * 5^4 =
5^3 * 3^2 * 4  /  3^4 * 5^4 =
4  /  3^2 * 5^1 =
4  /  9*5 =
4/45 ~ 0,089

5c)
2^8 * 5^7 / 100 =
2 * 2^7 * 5^7  / 10^2
2 * (2*5)^7    / 10^2
2 * 10^7  / 10^2
2 * 10^5 =
2 * 100000 = 200000

5d)
12^5 / 2^3 * 4^2 * 81 =
(3*4)^5 / (2^3 * 4^2 * 3^4) =
3^5 * 4^5 / (2^3 * 4^2 * 3^4) =
3^(5-4) * 4^(5-2) / 2^3 =
3 * 4^3 / 2^3 =
3 * (2^2)^3 / 2^3 =
3 * 2^6 / 2^3 =
3 * 2^(6-3) =
3 * 2^3 = 3 * 8 = 24

5e)
15^4 / 5^3 * 3^6
3^4 * 5^4 / 5^3 * 3^6
3^(4-6) * 5^(4-3) =
3^(-2) * 5 =
5/9

5f)
((3^2)^4 * 49^6) / (21^3 * 7^5) =
3^8 * (7^2)^6 / ((3*7)^3 * 7^5) =
3^8 * 7^12 / (3^3 * 7^3 * 7^5) =
3^(8-3) * 7^(12-3-5) =
3^5 * 7^4 =
583443