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  :

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  :

Multiplying exponents :

 4.1    2¹  multiplied by  2⁵   = 2^{(1 + 5)} = 2⁶

Equation at the end of step  4  :

Step  5  :

            (26•3•55)
 Simplify   —————————
            (3•22•52)

Dividing exponents :

 5.1    2⁶   divided by   2²   = 2^{(6 - 2)} = 2⁴

Canceling Out :

 5.2      Canceling out  3  as it appears on both sides of the fraction line

Dividing exponents :

 5.3    5⁵   divided by   5²   = 5^{(5 - 2)} = 5³

Final result :

  2000