Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "7.1" was replaced by "(71/10)". 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  :

   213       71
  (———•(104))——•(22•52))
   100(      10

Step  2  :

            71
 Simplify   ——
            10

Equation at the end of step  2  :

   213             71
  (——— • (104)) ÷ (—— • (22•52))
   100             10

Step  3  :

Dividing exponents :

 3.1    2²   divided by   2¹   = 2^{(2 - 1)} = 2¹ = 2

Raising to a Power :

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

Equation at the end of step  3  :

   213
  (——— • (104)) ÷ 710
   100

Step  4  :

 4.1     10 = 2•5

(10)⁴ = (2•5)⁴ = 2⁴ • 5⁴

Equation at the end of step  4  :

   213
  (——— • (24•54)) ÷ 710
   100

Step  5  :

            213
 Simplify   ———
            100

Equation at the end of step  5  :

  213
  ——— • (24•54)) ÷ 710
  100

Step  6  :

Dividing exponents :

 6.1    2⁴   divided by   2²   = 2^{(4 - 2)} = 2²

Dividing exponents :

 6.2    5⁴   divided by   5²   = 5^{(4 - 2)} = 5²

Equation at the end of step  6  :

Step  7  :

            (3•71•22•52)
 Simplify   ————————————
                710     

Canceling Out :

 7.1      Canceling out  71  as it appears on both sides of the fraction line

Dividing exponents :

 7.2    2²   divided by   2¹   = 2^{(2 - 1)} = 2¹ = 2

Dividing exponents :

 7.3    5²   divided by   5¹   = 5^{(2 - 1)} = 5¹ = 5

Final result :

  30