Solution - Power equations

Step  1  :

 1.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  1  :

  ((10-6) • (10-4)) • (23•53)

Step  2  :

 2.1     10 = 2•5

(10)^-4 = (2•5)^(-4) = (2)^(-4) • (5)^(-4)

Equation at the end of step  2  :

  ((10-6) • ((2)(-4)•(5)(-4))) • (23•53)

Step  3  :

 3.1     10 = 2•5

(10)^-6 = (2•5)^(-6) = (2)^(-6) • (5)^(-6)

Equation at the end of step  3  :

  (((2)(-6)•(5)(-6)) • ((2)(-4)•(5)(-4))) • (23•53)
 Step  4  :

Dividing exponents :

 4.1    2³   divided by   2¹⁰   = 2^{(3 - 10)} = 2^(-7) = ¹/_2⁷

Dividing exponents :

 4.2    5³   divided by   5¹⁰   = 5^{(3 - 10)} = 5^(-7) = ¹/_5⁷

Final result :

     1                                      
  ——————— = 10.00000 • 10-8 
  (27•57)