Question

S the expression x3•x3•x3 equivalent to x3•3•3

Answer 1

Remember
(x^m)(x^n)=x^(m+n)
and difference of 2 perfect squres
(a²-b²)=(a-b)(a+b)
and sum or difference of 2 perfect cubes

so
(x^3)(x^3)(x^3)=x^(3+3+3)=x^9
so

x^9=3*3*x^3
x^9=9x^3
minus 9x^3 both sides
0=x^9-9x^3
factor
0=(x^3)(x^6-9)
factor difference of 2 perfect squraes
0=(x^3)(x^3-3)(x^3+3)
factor differnce or sum of 2 perfect cubes (force 3 into (∛3)³)
0=(x³)(x-∛3)(x²+x∛3+∛9)(x+∛3)(x²-x∛3+∛9)
set each to zero

x³=0
x=0

x-∛3=0
x=∛3

x²+x∛3+∛9=0 has no solution

x+∛3=0
x=-∛3

x²-x∛3+∛9=0 has no solution



so the solutions are
x=-∛3, 0, ∛3