Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-3" was replaced by "^(-3)".

(2): "1.5" was replaced by "(15/10)".

Step  1  :

 1.1     10 = 2•5

(10)^-3 = (2•5)^(-3) = (2)^(-3) • (5)^(-3)

Equation at the end of step  1  :

      15
  ((((——•x)•(108))•2)•x)•((2)(-3)•(5)(-3))
      10

Step  2  :

 2.1     10 = 2•5

(10)⁸ = (2•5)⁸ = 2⁸ • 5⁸

Equation at the end of step  2  :

      15
  ((((——•x)•(28•58))•2)•x)•((2)(-3)•(5)(-3))
      10

Step  3  :

            3
 Simplify   —
            2

Equation at the end of step  3  :

      3
  ((((— • x) • (28•58)) • 2) • x) • ((2)(-3)•(5)(-3))
      2

Step  4  :

Dividing exponents :

 4.1    2⁸   divided by   2¹   = 2^{(8 - 1)} = 2⁷

Equation at the end of step  4  :

  (((3•27•58x) • 2) • x) • ((2)(-3)•(5)(-3))

Step  5  :

Multiplying exponents :

 5.1    2⁷  multiplied by  2¹   = 2^{(7 + 1)} = 2⁸

Equation at the end of step  5  :

  ((3•28•58x) • x) • ((2)(-3)•(5)(-3))
 Step  6  :

Dividing exponents :

 6.1    2⁸   divided by   2³   = 2^{(8 - 3)} = 2⁵

Dividing exponents :

 6.2    5⁸   divided by   5³   = 5^{(8 - 3)} = 5⁵

Final result :

  (3•25•55x2)