Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-8" was replaced by "^(-8)". 1 more similar replacement(s)

(2): "1.4" was replaced by "(14/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

    72         14
  ((——•(10-7))•——)•((2)(-8)•(5)(-8))
    10         10

Step  2  :

            7
 Simplify   —
            5

Equation at the end of step  2  :

    72             7
  ((—— • (10-7)) • —) • ((2)(-8)•(5)(-8))
    10             5

Step  3  :

 3.1     10 = 2•5

(10)^-7 = (2•5)^(-7) = (2)^(-7) • (5)^(-7)

Equation at the end of step  3  :

    72                        7
  ((—— • ((2)(-7)•(5)(-7))) • —) • ((2)(-8)•(5)(-8))
    10                        5

Step  4  :

            36
 Simplify   ——
            5 

Equation at the end of step  4  :

    36                        7
  ((—— • ((2)(-7)•(5)(-7))) • —) • ((2)(-8)•(5)(-8))
    5                         5

Step  5  :

Multiplying exponents :

 5.1    5¹  multiplied by  5⁷   = 5^{(1 + 7)} = 5⁸

Dividing exponents :

 5.2    2²   divided by   2⁷   = 2^{(2 - 7)} = 2^(-5) = ¹/_2⁵

Equation at the end of step  5  :

      9      7
  (——————— • —) • ((2)(-8)•(5)(-8))
   (58•25)   5

Step  6  :

Multiplying exponents :

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

Equation at the end of step  6  :

     63  
  ——————— • ((2)(-8)•(5)(-8))
  (59•25)

Step  7  :

Multiplying exponents :

 7.1    5⁹  multiplied by  5⁸   = 5^{(9 + 8)} = 5¹⁷

Multiplying exponents :

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

Final result :

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