Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-2" was replaced by "^(-2)".

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

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

   15
  (—— • (107)) ÷ (5 • ((2)(-2)•(5)(-2)))
   10

Step  2  :

Raising to a Power :

 2.1    5¹   divided by   5²   = 5^{(1 - 2)} = 5^(-1) = ¹/_5¹ = ¹/₅

Equation at the end of step  2  :

   15             1
  (—— • (107)) ÷ ——
   10            20

Step  3  :

 3.1     10 = 2•5

(10)⁷ = (2•5)⁷ = 2⁷ • 5⁷

Equation at the end of step  3  :

   15               1
  (—— • (27•57)) ÷ ——
   10              20

Step  4  :

            3
 Simplify   —
            2

Equation at the end of step  4  :

  3               1
  — • (27•57)) ÷ ——
  2              20

Step  5  :

Dividing exponents :

 5.1    2⁷   divided by   2¹   = 2^{(7 - 1)} = 2⁶

Equation at the end of step  5  :

  )1
  ——
  20

Step  6  :

                         1
 Divide  (3•26•57)  by  ——
                        20

Multiplying exponents :

 6.1    2⁶  multiplied by  2²   = 2^{(6 + 2)} = 2⁸

Multiplying exponents :

 6.2    5⁷  multiplied by  5¹   = 5^{(7 + 1)} = 5⁸

Final result :

  (3•28•58)