Solution - Power equations

Step  1  :

 1.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  1  :

Step  2  :

Raising to a Power :

 2.1    2²  multiplied by  2³   = 2^{(2 + 3)} = 2⁵

Equation at the end of step  2  :

Step  3  :

 3.1     10 = 2•5

(10)⁴ = (2•5)⁴ = 2⁴ • 5⁴

Equation at the end of step  3  :

Step  4  :

Multiplying exponents :

 4.1    2³  multiplied by  2⁴   = 2^{(3 + 4)} = 2⁷

Equation at the end of step  4  :

Step  5  :

            (27•54)
 Simplify   ———————
            (25•53)

Dividing exponents :

 5.1    2⁷   divided by   2⁵   = 2^{(7 - 5)} = 2²

Dividing exponents :

 5.2    5⁴   divided by   5³   = 5^{(4 - 3)} = 5¹ = 5

Final result :

  20