Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-3" was replaced by "^(-3)". 1 more similar replacement(s)

(2): "4." was replaced by "(4/1)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)^-3 = (2•5)^(-3) = (2)^(-3) • (5)^(-3)

Equation at the end of step  1  :

    12         4
  ((——•(10-8))•—)•((2)(-3)•(5)(-3))
    10         1

Step  2  :

            4
 Simplify   —
            1

Equation at the end of step  2  :

    12
  ((—— • (10-8)) • 4) • ((2)(-3)•(5)(-3))
    10

Step  3  :

 3.1     10 = 2•5

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

Equation at the end of step  3  :

    12
  ((—— • ((2)(-8)•(5)(-8))) • 4) • ((2)(-3)•(5)(-3))
    10

Step  4  :

            6
 Simplify   —
            5

Equation at the end of step  4  :

    6
  ((— • ((2)(-8)•(5)(-8))) • 4) • ((2)(-3)•(5)(-3))
    5

Step  5  :

Multiplying exponents :

 5.1    5¹  multiplied by  5⁸   = 5^{(1 + 8)} = 5⁹

Dividing exponents :

 5.2    2¹   divided by   2⁸   = 2^{(1 - 8)} = 2^(-7) = ¹/_2⁷

Equation at the end of step  5  :

      3   
  (——————— • 4) • ((2)(-3)•(5)(-3))
   (59•27)

Step  6  :

Dividing exponents :

 6.1    2²   divided by   2⁷   = 2^{(2 - 7)} = 2^(-5) = ¹/_2⁵

Equation at the end of step  6  :

     3   
  ——————— • ((2)(-3)•(5)(-3))
  (59•25)

Step  7  :

Multiplying exponents :

 7.1    5⁹  multiplied by  5³   = 5^{(9 + 3)} = 5¹²

Multiplying exponents :

 7.2    2⁵  multiplied by  2³   = 2^{(5 + 3)} = 2⁸

Final result :

      3                                      
  ———————— = 4.80000 • 10-11 
  (512•28)