Solution - Power equations

Step  1  :

 1.1     10 = 2•5

(10)¹ = (2•5)¹ = 2 • 5

Equation at the end of step  1  :

Step  2  :

Raising to a Power :

 2.1    2²  multiplied by  2¹   = 2^{(2 + 1)} = 2³

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    2²  multiplied by  2²   = 2^{(2 + 2)} = 2⁴

Equation at the end of step  4  :

Step  5  :

            (24•52)
 Simplify   ———————
            (23•5) 

Dividing exponents :

 5.1    2⁴   divided by   2³   = 2^{(4 - 3)} = 2¹ = 2

Dividing exponents :

 5.2    5²   divided by   5¹   = 5^{(2 - 1)} = 5¹ = 5

Final result :

  10