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  :

Raising to a Power :

 2.1    2²  multiplied by  2⁷   = 2^{(2 + 7)} = 2⁹

Equation at the end of step  2  :

Step  3  :

 3.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  3  :

Step  4  :

Equation at the end of step  4  :

Step  5  :

            (32•25•55)
 Simplify   ——————————
             (29•57)  

Dividing exponents :

 5.1    2⁵   divided by   2⁹   = 2^{(5 - 9)} = 2^(-4) = ¹/_2⁴

Dividing exponents :

 5.2    5⁵   divided by   5⁷   = 5^{(5 - 7)} = 5^(-2) = ¹/_5²

Final result :

   9            
  ——— = 0.02250 
  400