Solution - Power equations

Step  1  :

 1.1     10 = 2•5

(10)⁴ = (2•5)⁴ = 2⁴ • 5⁴

Equation at the end of step  1  :

Step  2  :

Raising to a Power :

 2.1    2³  multiplied by  2⁴   = 2^{(3 + 4)} = 2⁷

Equation at the end of step  2  :

Step  3  :

 3.1     10 = 2•5

(10)¹ = (2•5)¹ = 2 • 5

Equation at the end of step  3  :

Step  4  :

Multiplying exponents :

 4.1    2³  multiplied by  2¹   = 2^{(3 + 1)} = 2⁴

Equation at the end of step  4  :

Step  5  :

             (24•5)
 Simplify   ———————
            (27•54)

Dividing exponents :

 5.1    2⁴   divided by   2⁷   = 2^{(4 - 7)} = 2^(-3) = ¹/_2³

Dividing exponents :

 5.2    5¹   divided by   5⁴   = 5^{(1 - 4)} = 5^(-3) = ¹/_5³

Final result :

    1            
  ———— = 0.00100 
  1000