Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-5" was replaced by "^(-5)".

(2): "4.9" was replaced by "(49/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

   77         49
  (——•(108))•(——•((2)(-5)•(5)(-5)))
   10         10

Step  2  :

            49
 Simplify   ——
            10

Equation at the end of step  2  :

   77             49
  (—— • (108)) • (—— • ((2)(-5)•(5)(-5)))
   10             10

Step  3  :

Multiplying exponents :

 3.1    2¹  multiplied by  2⁵   = 2^{(1 + 5)} = 2⁶

Raising to a Power :

 3.2    5¹  multiplied by  5⁵   = 5^{(1 + 5)} = 5⁶

Equation at the end of step  3  :

   77               49  
  (—— • (108)) • ———————
   10            (26•56)

Step  4  :

 4.1     10 = 2•5

(10)⁸ = (2•5)⁸ = 2⁸ • 5⁸

Equation at the end of step  4  :

   77                 49  
  (—— • (28•58)) • ———————
   10              (26•56)

Step  5  :

            77
 Simplify   ——
            10

Equation at the end of step  5  :

   77                 49  
  (—— • (28•58)) • ———————
   10              (26•56)

Step  6  :

Dividing exponents :

 6.1    2⁸   divided by   2¹   = 2^{(8 - 1)} = 2⁷

Dividing exponents :

 6.2    5⁸   divided by   5¹   = 5^{(8 - 1)} = 5⁷

Equation at the end of step  6  :

                    49  
  (7•11•27•57) • ———————
                 (26•56)

Step  7  :

Multiplying exponents :

 7.1    7¹  multiplied by  7²   = 7^{(1 + 2)} = 7³

Dividing exponents :

 7.2    2⁷   divided by   2⁶   = 2^{(7 - 6)} = 2¹ = 2

Dividing exponents :

 7.3    5⁷   divided by   5⁶   = 5^{(7 - 6)} = 5¹ = 5

Final result :

  (73•11•2•5)