Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-5" was replaced by "^(-5))". 1 more similar replacement(s)

(2): "4.2" was replaced by "(42/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

    24          42
  ((——•(10-10))•——)•((2)(-5)•(5)(-5))
    10          10

Step  2  :

            21
 Simplify   ——
            5 

Equation at the end of step  2  :

    24              21
  ((—— • (10-10)) • ——) • ((2)(-5)•(5)(-5))
    10              5 

Step  3  :

 3.1     10 = 2•5

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

Equation at the end of step  3  :

    24                          21
  ((—— • ((2)(-10)•(5)(-10))) • ——) • ((2)(-5)•(5)(-5))
    10                          5 

Step  4  :

            12
 Simplify   ——
            5 

Equation at the end of step  4  :

    12                          21
  ((—— • ((2)(-10)•(5)(-10))) • ——) • ((2)(-5)•(5)(-5))
    5                           5 

Step  5  :

Multiplying exponents :

 5.1    5¹  multiplied by  5¹⁰   = 5^{(1 + 10)} = 5¹¹

Dividing exponents :

 5.2    2²   divided by   2¹⁰   = 2^{(2 - 10)} = 2^(-8) = ¹/_2⁸

Equation at the end of step  5  :

       3      21
  (———————— • ——) • ((2)(-5)•(5)(-5))
   (511•28)    5 

Step  6  :

Multiplying exponents :

 6.1    5¹¹  multiplied by  5¹   = 5^{(11 + 1)} = 5¹²

Equation at the end of step  6  :

     63   
  ———————— • ((2)(-5)•(5)(-5))
  (512•28) 

Step  7  :

Multiplying exponents :

 7.1    5¹²  multiplied by  5⁵   = 5^{(12 + 5)} = 5¹⁷

Multiplying exponents :

 7.2    2⁸  multiplied by  2⁵   = 2^{(8 + 5)} = 2¹³

Final result :

      63                                      
  ————————— = 1.00800 • 10-14 
  (517•213)