Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "2." was replaced by "(2/1)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

    5        2
  ((—•(106))•—)•((2)(-2)•(5)(-2))
    1        1

Step  2  :

            2
 Simplify   —
            1

Equation at the end of step  2  :

    5
  ((— • (106)) • 2) • ((2)(-2)•(5)(-2))
    1

Step  3  :

 3.1     10 = 2•5

(10)⁶ = (2•5)⁶ = 2⁶ • 5⁶

Equation at the end of step  3  :

    5
  ((— • (26•56)) • 2) • ((2)(-2)•(5)(-2))
    1

Step  4  :

            5
 Simplify   —
            1

Equation at the end of step  4  :

  ((5 • (26•56)) • 2) • ((2)(-2)•(5)(-2))

Step  5  :

Multiplying exponents :

 5.1    5¹  multiplied by  5⁶   = 5^{(1 + 6)} = 5⁷

Equation at the end of step  5  :

  ((57•26) • 2) • ((2)(-2)•(5)(-2))

Step  6  :

Multiplying exponents :

 6.1    2⁶  multiplied by  2¹   = 2^{(6 + 1)} = 2⁷

Equation at the end of step  6  :

  (57•27) • ((2)(-2)•(5)(-2))

Step  7  :

Dividing exponents :

 7.1    5⁷   divided by   5²   = 5^{(7 - 2)} = 5⁵

Dividing exponents :

 7.2    2⁷   divided by   2²   = 2^{(7 - 2)} = 2⁵

Final result :

  (55•25)