Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-34" was replaced by "^(-34)".

(2): "7.5" was replaced by "(75/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)⁸ = (2•5)⁸ = 2⁸ • 5⁸

Equation at the end of step  1  :

    66          75
  ((——•(10-34))•——)•(28•58)
    10          10

Step  2  :

            15
 Simplify   ——
            2 

Equation at the end of step  2  :

    66              15
  ((—— • (10-34)) • ——) • (28•58)
    10              2 

Step  3  :

 3.1     10 = 2•5

(10)^-34 = (2•5)^(-34) = (2)^(-34) • (5)^(-34)

Equation at the end of step  3  :

    66                          15
  ((—— • ((2)(-34)•(5)(-34))) • ——) • (28•58)
    10                          2 

Step  4  :

            33
 Simplify   ——
            5 

Equation at the end of step  4  :

    33                          15
  ((—— • ((2)(-34)•(5)(-34))) • ——) • (28•58)
    5                           2 

Step  5  :

Multiplying exponents :

 5.1    5¹  multiplied by  5³⁴   = 5^{(1 + 34)} = 5³⁵

Equation at the end of step  5  :

       33      15
  (————————— • ——) • (28•58)
   (535•234)    2 

Step  6  :

Multiplying exponents :

 6.1    2³⁴  multiplied by  2¹   = 2^{(34 + 1)} = 2³⁵

Dividing exponents :

 6.2    5¹   divided by   5³⁵   = 5^{(1 - 35)} = 5^(-34) = ¹/_5³⁴

Equation at the end of step  6  :

      99   
  ————————— • (28•58)
  (534•235) 

Step  7  :

Dividing exponents :

 7.1    2⁸   divided by   2³⁵   = 2^{(8 - 35)} = 2^(-27) = ¹/_2²⁷

Dividing exponents :

 7.2    5⁸   divided by   5³⁴   = 5^{(8 - 34)} = 5^(-26) = ¹/_5²⁶

Final result :

      99                                      
  ————————— = 4.95000 • 10-25 
  (526•227)