Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "4.8" was replaced by "(48/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  1  :

   3168       48
  (————•(109))——•(22•52))
   1000(      10

Step  2  :

            24
 Simplify   ——
            5 

Equation at the end of step  2  :

   3168             24
  (———— • (109)) ÷ (—— • (22•52))
   1000             5 

Step  3  :

Multiplying exponents :

 3.1    2³  multiplied by  2²   = 2^{(3 + 2)} = 2⁵

Raising to a Power :

 3.2    5²   divided by   5¹   = 5^{(2 - 1)} = 5¹ = 5

Equation at the end of step  3  :

   3168
  (———— • (109)) ÷ 480
   1000

Step  4  :

 4.1     10 = 2•5

(10)⁹ = (2•5)⁹ = 2⁹ • 5⁹

Equation at the end of step  4  :

   3168
  (———— • (29•59)) ÷ 480
   1000

Step  5  :

            396
 Simplify   ———
            125

Equation at the end of step  5  :

  396
  ——— • (29•59)) ÷ 480
  125

Step  6  :

Multiplying exponents :

 6.1    2²  multiplied by  2⁹   = 2^{(2 + 9)} = 2¹¹

Dividing exponents :

 6.2    5⁹   divided by   5³   = 5^{(9 - 3)} = 5⁶

Equation at the end of step  6  :

Step  7  :

            (211•32•11•56) 
 Simplify   ——————————————
                 480      

Dividing exponents :

 7.1    2¹¹   divided by   2⁵   = 2^{(11 - 5)} = 2⁶

Dividing exponents :

 7.2    3²   divided by   3¹   = 3^{(2 - 1)} = 3¹ = 3

Dividing exponents :

 7.3    5⁶   divided by   5¹   = 5^{(6 - 1)} = 5⁵

Final result :

  (26•3•11•55)