Explicație pas cu pas:
1.a)
[tex] = 0 + 1 + 1 + 13 = 15[/tex]
b)
[tex]= {2}^{22 - 20} = {2}^{2} = 4[/tex]
c)
[tex]= {( {3}^{2} )}^{60} \div {3}^{120} + 1 = {3}^{2 \times 60} \div {3}^{120} + 1\\ = {3}^{120} \div {3}^{120} + 1 = 1 + 1 = 2[/tex]
d)
[tex]= {5}^{100} \div {( {5}^{3} )}^{33} = {5}^{100} \div {5}^{3 \times 33} = {5}^{100} \div {5}^{99} \\ = {5}^{100 - 99} = {5}^{1} = 5[/tex]
2.
{120 - 2 • [14 + 5 • (x - 3)]}} : 4 = 8
120 - 2 • [14 + 5 • (x - 3)]} = 8 • 4
120 - 2 • [14 + 5 • (x - 3)]} = 32
2 • [14 + 5 • (x - 3)]} = 120 - 32
2 • [14 + 5 • (x - 3)]} = 88
14 + 5 • (x - 3) = 88 : 2
14 + 5 • (x - 3) = 44
5 • (x - 3) = 44 - 14
5 • (x - 3) = 30
x - 3 = 30 : 5
x - 3 = 6
x = 6 + 3
x = 9
3. a = 2•3³•6⁵ = 2•3³•(2•3)⁵ = 2•3³•2⁵•3⁵ = 2⁶•3⁸
= (2³)²•(3⁴)² = (2³•3⁴)²
=> a este pătrat perfect
