Solution - Power equations

Step  1  :

 1.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  1  :

Step  2  :

Raising to a Power :

 2.1    5¹  multiplied by  5²   = 5^{(1 + 2)} = 5³

Equation at the end of step  2  :

Step  3  :

 3.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  3  :

Step  4  :

Multiplying exponents :

 4.1    2³  multiplied by  2²   = 2^{(3 + 2)} = 2⁵

Equation at the end of step  4  :

Step  5  :

            ( -25•52)
 Simplify   —————————
            ( -53•22)

Dividing exponents :

 5.1    2⁵   divided by   2²   = 2^{(5 - 2)} = 2³

Dividing exponents :

 5.2    5²   divided by   5³   = 5^{(2 - 3)} = 5^(-1) = ¹/_5¹ = ¹/₅

Final result :

  8           
  — = 1.60000 
  5