[(25*2^2)^2-(2^3*3*2^2)^2-(7*2^2)^2]^6

Question

[(25*2^2)^2-(2^3*3*2^2)^2-(7*2^2)^2]^6

Answer 1

[(25*2^2)^2-(2^3*3*2^2)^2-(7*2^2)^2]^6
=
[ (5^2• 2^2- 2^3 •3• 2^2- 7^2• 2^2)^2]^6=

[ {2^2 • (5^2- 2^3• 3- 7^2) }^2 ]^6=

[{ 2^2• (5•5- 2•2•2•3- 7•7)}^2]^6=

[{2^2•(25-24-49)}^2 ]^6=

[{2^2• (-50)}^2]^6=

[{2^2• (-(5•5•2)}^2]^6=

Степень четная (-) исчезнет
[ (2•2• 5•5•2)^2]*6=

[(10•10•2)^2]^6=

[(10^2• 2)^2]^6=

[10^4• 2^2]^6=

10^24• 2^12 =

(10^2)^12• 2^12=

(100•2)^12=

200^12=

200.000.000.000.000