Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-3" was replaced by "^(-3)".

(2): "4.1" was replaced by "(41/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)^-3 = (2•5)^(-3) = (2)^(-3) • (5)^(-3)

Equation at the end of step  1  :

   523         41
  (———•(106))•(——•((2)(-3)•(5)(-3)))
   100         10

Step  2  :

            41
 Simplify   ——
            10

Equation at the end of step  2  :

   523             41
  (——— • (106)) • (—— • ((2)(-3)•(5)(-3)))
   100             10

Step  3  :

Multiplying exponents :

 3.1    2¹  multiplied by  2³   = 2^{(1 + 3)} = 2⁴

Raising to a Power :

 3.2    5¹  multiplied by  5³   = 5^{(1 + 3)} = 5⁴

Equation at the end of step  3  :

   523               41  
  (——— • (106)) • ———————
   100            (24•54)

Step  4  :

 4.1     10 = 2•5

(10)⁶ = (2•5)⁶ = 2⁶ • 5⁶

Equation at the end of step  4  :

   523                 41  
  (——— • (26•56)) • ———————
   100              (24•54)

Step  5  :

            523
 Simplify   ———
            100

Equation at the end of step  5  :

   523                 41  
  (——— • (26•56)) • ———————
   100              (24•54)

Step  6  :

Dividing exponents :

 6.1    2⁶   divided by   2²   = 2^{(6 - 2)} = 2⁴

Dividing exponents :

 6.2    5⁶   divided by   5²   = 5^{(6 - 2)} = 5⁴

Equation at the end of step  6  :

                   41  
  (523•24•54) • ———————
                (24•54)

Step  7  :

Canceling Out :

 7.1      Canceling out  2⁴ as it appears on both sides of the fraction line

Canceling Out :

 7.2      Canceling out  5⁴ as it appears on both sides of the fraction line

Final result :

  (523•41)