Question

Va rog sa ma ajutati! Am nevoie de exercitiul: 2^101 × 5^99 + 10^99 - 2^99 × 5^100 unde ^ este semn de ridicare la putere

Answer 1

2¹⁰¹x5⁹⁹+10⁹⁹-2⁹⁹x5¹⁰⁰=
=2⁹⁹x2²x5⁹⁹+(2x5)⁹⁹-2⁹⁹x5⁹⁹x5=
=2⁹⁹x2²x5⁹⁹+2⁹⁹x5⁹⁹-2⁹⁹x5⁹⁹x5=
=2⁹⁹x5⁹⁹(2²+1-5)=
=10⁹⁹x0=
=0

Answer 2

2^101 x5^99 +10^99 - 2^99 x5^100= 0
2^99 x2^2 x5^99 + (2x5)^99 - 2^99 x 5^99 x5^1=
2^99 x2^2 x5^99 +2^99 x 5^99 - 2^99 x 5^99 x5=
2^99 x 5^99 x (2^2+1 -5)=
2^99 x5^99 x0=0