Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-2" was replaced by "^(-2)".

(2): "2.4" was replaced by "(24/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  1  :

   691          24
  (———•(10-2))•(——•(23•53))
   100          10

Step  2  :

            12
 Simplify   ——
            5 

Equation at the end of step  2  :

   691              12
  (——— • (10-2)) • (—— • (23•53))
   100              5 

Step  3  :

Multiplying exponents :

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

Raising to a Power :

 3.2    5³   divided by   5¹   = 5^{(3 - 1)} = 5²

Equation at the end of step  3  :

   691
  (——— • (10-2)) • 2400
   100

Step  4  :

 4.1     10 = 2•5

(10)^-2 = (2•5)^(-2) = (2)^(-2) • (5)^(-2)

Equation at the end of step  4  :

   691
  (——— • ((2)(-2)•(5)(-2))) • 2400
   100

Step  5  :

            691
 Simplify   ———
            100

Equation at the end of step  5  :

   691
  (——— • ((2)(-2)•(5)(-2))) • 2400
   100

Step  6  :

Multiplying exponents :

 6.1    2²  multiplied by  2²   = 2^{(2 + 2)} = 2⁴

Multiplying exponents :

 6.2    5²  multiplied by  5²   = 5^{(2 + 2)} = 5⁴

Equation at the end of step  6  :

    691  
  ——————— • 2400
  (24•54)

Step  7  :

Dividing exponents :

 7.1    2⁵   divided by   2⁴   = 2^{(5 - 4)} = 2¹ = 2

Dividing exponents :

 7.2    5²   divided by   5⁴   = 5^{(2 - 4)} = 5^(-2) = ¹/_5²

Final result :

  4146             
  ———— = 165.84000 
   25