Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "1.6" was replaced by "(16/10)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

                 16
  ((8 • (105)) • ——) • ((2)(-2)•(5)(-2))
                 10

Step  2  :

            8
 Simplify   —
            5

Equation at the end of step  2  :

                 8
  ((8 • (105)) • —) • ((2)(-2)•(5)(-2))
                 5

Step  3  :

 3.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  3  :

                   8
  ((8 • (25•55)) • —) • ((2)(-2)•(5)(-2))
                   5

Step  4  :

Multiplying exponents :

 4.1    2³  multiplied by  2⁵   = 2^{(3 + 5)} = 2⁸

Equation at the end of step  4  :

             8
  ((28•55) • —) • ((2)(-2)•(5)(-2))
             5

Step  5  :

Multiplying exponents :

 5.1    2⁸  multiplied by  2³   = 2^{(8 + 3)} = 2¹¹

Dividing exponents :

 5.2    5⁵   divided by   5¹   = 5^{(5 - 1)} = 5⁴

Equation at the end of step  5  :

  (211•54) • ((2)(-2)•(5)(-2))

Step  6  :

Dividing exponents :

 6.1    2¹¹   divided by   2²   = 2^{(11 - 2)} = 2⁹

Dividing exponents :

 6.2    5⁴   divided by   5²   = 5^{(4 - 2)} = 5²

Final result :

  (29•52)