Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "4.24" was replaced by "(424/100)". 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  :

    9926        424
  ((————•(105))•———)•((2)(-2)•(5)(-2))
    1000        100

Step  2  :

            106
 Simplify   ———
            25 

Equation at the end of step  2  :

    9926            106
  ((———— • (105)) • ———) • ((2)(-2)•(5)(-2))
    1000            25 

Step  3  :

 3.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  3  :

    9926              106
  ((———— • (25•55)) • ———) • ((2)(-2)•(5)(-2))
    1000              25 

Step  4  :

            4963
 Simplify   ————
            500 

Equation at the end of step  4  :

    4963              106
  ((———— • (25•55)) • ———) • ((2)(-2)•(5)(-2))
    500               25 

Step  5  :

Dividing exponents :

 5.1    2⁵   divided by   2²   = 2^{(5 - 2)} = 2³

Dividing exponents :

 5.2    5⁵   divided by   5³   = 5^{(5 - 3)} = 5²

Equation at the end of step  5  :

                   106
  ((7•709•23•52) • ———) • ((2)(-2)•(5)(-2))
                   25 

Step  6  :

Multiplying exponents :

 6.1    2³  multiplied by  2¹   = 2^{(3 + 1)} = 2⁴

Canceling Out :

 6.2      Canceling out  5² as it appears on both sides of the fraction line

Equation at the end of step  6  :

  (7•709•24•53) • ((2)(-2)•(5)(-2))

Step  7  :

Dividing exponents :

 7.1    2⁴   divided by   2²   = 2^{(4 - 2)} = 2²

Final result :

  (7•709•22•53)               
  ————————————— = 42086.24000 
       25