Solution - Power equations

Step  1  :

 1.1     10 = 2•5

(10)⁷ = (2•5)⁷ = 2⁷ • 5⁷

Equation at the end of step  1  :

Step  2  :

Equation at the end of step  2  :

Step  3  :

 3.1     10 = 2•5

(10)⁴ = (2•5)⁴ = 2⁴ • 5⁴

Equation at the end of step  3  :

Step  4  :

Equation at the end of step  4  :

Step  5  :

            (32•24•54)
 Simplify   ——————————
            (3•27•57) 

Dividing exponents :

 5.1    3²   divided by   3¹   = 3^{(2 - 1)} = 3¹ = 3

Dividing exponents :

 5.2    2⁴   divided by   2⁷   = 2^{(4 - 7)} = 2^(-3) = ¹/_2³

Dividing exponents :

 5.3    5⁴   divided by   5⁷   = 5^{(4 - 7)} = 5^(-3) = ¹/_5³

Final result :

    3            
  ———— = 0.00300 
  1000