Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-4" was replaced by "^(-4)".

(2): "6.2" was replaced by "(62/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)^-4 = (2•5)^(-4) = (2)^(-4) • (5)^(-4)

Equation at the end of step  1  :

    24        62
  ((——•(106))•——)•((2)(-4)•(5)(-4))
    10        10

Step  2  :

            31
 Simplify   ——
            5 

Equation at the end of step  2  :

    24            31
  ((—— • (106)) • ——) • ((2)(-4)•(5)(-4))
    10            5 

Step  3  :

 3.1     10 = 2•5

(10)⁶ = (2•5)⁶ = 2⁶ • 5⁶

Equation at the end of step  3  :

    24              31
  ((—— • (26•56)) • ——) • ((2)(-4)•(5)(-4))
    10              5 

Step  4  :

            12
 Simplify   ——
            5 

Equation at the end of step  4  :

    12              31
  ((—— • (26•56)) • ——) • ((2)(-4)•(5)(-4))
    5               5 

Step  5  :

Multiplying exponents :

 5.1    2²  multiplied by  2⁶   = 2^{(2 + 6)} = 2⁸

Dividing exponents :

 5.2    5⁶   divided by   5¹   = 5^{(6 - 1)} = 5⁵

Equation at the end of step  5  :

               31
  ((28•3•55) • ——) • ((2)(-4)•(5)(-4))
               5 

Step  6  :

Dividing exponents :

 6.1    5⁵   divided by   5¹   = 5^{(5 - 1)} = 5⁴

Equation at the end of step  6  :

  (28•3•54•31) • ((2)(-4)•(5)(-4))

Step  7  :

Dividing exponents :

 7.1    2⁸   divided by   2⁴   = 2^{(8 - 4)} = 2⁴

Canceling Out :

 7.2      Canceling out  5⁴ as it appears on both sides of the fraction line

Final result :

  1488