Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "4.1" was replaced by "(41/10)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

    41
  ((—— • (105)) • 3) • ((2)(-3)•(5)(-3))
    10

Step  2  :

 2.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  2  :

    41
  ((—— • (25•55)) • 3) • ((2)(-3)•(5)(-3))
    10

Step  3  :

            41
 Simplify   ——
            10

Equation at the end of step  3  :

    41
  ((—— • (25•55)) • 3) • ((2)(-3)•(5)(-3))
    10

Step  4  :

Dividing exponents :

 4.1    2⁵   divided by   2¹   = 2^{(5 - 1)} = 2⁴

Dividing exponents :

 4.2    5⁵   divided by   5¹   = 5^{(5 - 1)} = 5⁴

Equation at the end of step  4  :

  ((41•24•54) • 3) • ((2)(-3)•(5)(-3))

Step  5  :

Equation at the end of step  5  :

  (41•24•54•3) • ((2)(-3)•(5)(-3))

Step  6  :

Dividing exponents :

 6.1    2⁴   divided by   2³   = 2^{(4 - 3)} = 2¹ = 2

Dividing exponents :

 6.2    5⁴   divided by   5³   = 5^{(4 - 3)} = 5¹ = 5

Final result :

  1230