Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "8.2" was replaced by "(82/10)".

Step  1  :

 1.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  1  :

    82
  ((—— • (102)) • 4) • (23•53)
    10

Step  2  :

 2.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  2  :

    82
  ((—— • (22•52)) • 4) • (23•53)
    10

Step  3  :

            41
 Simplify   ——
            5 

Equation at the end of step  3  :

    41
  ((—— • (22•52)) • 4) • (23•53)
    5 

Step  4  :

Dividing exponents :

 4.1    5²   divided by   5¹   = 5^{(2 - 1)} = 5¹ = 5

Equation at the end of step  4  :

  (820 • 4) • (23•53)

Step  5  :

Multiplying exponents :

 5.1    2⁴  multiplied by  2³   = 2^{(4 + 3)} = 2⁷

Multiplying exponents :

 5.2    5¹  multiplied by  5³   = 5^{(1 + 3)} = 5⁴

Final result :

  (27•54•41)