Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-8" was replaced by "^(-8)".

(2): "6.4" was replaced by "(64/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  1  :

    925         64
  ((———•(10-8))•——)•(23•53)
    100         10

Step  2  :

            32
 Simplify   ——
            5 

Equation at the end of step  2  :

    925             32
  ((——— • (10-8)) • ——) • (23•53)
    100             5 

Step  3  :

 3.1     10 = 2•5

(10)^-8 = (2•5)^(-8) = (2)^(-8) • (5)^(-8)

Equation at the end of step  3  :

    925                        32
  ((——— • ((2)(-8)•(5)(-8))) • ——) • (23•53)
    100                        5 

Step  4  :

            37
 Simplify   ——
            4 

Equation at the end of step  4  :

    37                        32
  ((—— • ((2)(-8)•(5)(-8))) • ——) • (23•53)
    4                         5 

Step  5  :

Multiplying exponents :

 5.1    2²  multiplied by  2⁸   = 2^{(2 + 8)} = 2¹⁰

Equation at the end of step  5  :

      37      32
  (———————— • ——) • (23•53)
   (210•58)    5 

Step  6  :

Multiplying exponents :

 6.1    5⁸  multiplied by  5¹   = 5^{(8 + 1)} = 5⁹

Dividing exponents :

 6.2    2⁵   divided by   2¹⁰   = 2^{(5 - 10)} = 2^(-5) = ¹/_2⁵

Equation at the end of step  6  :

     37  
  ——————— • (23•53)
  (25•59)

Step  7  :

Dividing exponents :

 7.1    2³   divided by   2⁵   = 2^{(3 - 5)} = 2^(-2) = ¹/_2²

Dividing exponents :

 7.2    5³   divided by   5⁹   = 5^{(3 - 9)} = 5^(-6) = ¹/_5⁶

Final result :

     37             
  ——————— = 0.00059 
  (22•56)