Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-5" was replaced by "^(-5)". 1 more similar replacement(s)

(2): "7.2" was replaced by "(72/10)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

   72
  (—— • (10-3)) ÷ (4 • ((2)(-5)•(5)(-5)))
   10

Step  2  :

Raising to a Power :

 2.1    2²   divided by   2⁵   = 2^{(2 - 5)} = 2^(-3) = ¹/_2³

Equation at the end of step  2  :

   72                1   
  (—— • (10-3)) ÷ ———————
   10             (23•55)

Step  3  :

 3.1     10 = 2•5

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

Equation at the end of step  3  :

   72                           1   
  (—— • ((2)(-3)•(5)(-3))) ÷ ———————
   10                        (23•55)

Step  4  :

            36
 Simplify   ——
            5 

Equation at the end of step  4  :

  36                           1   
  —— • ((2)(-3)•(5)(-3))) ÷ ———————
  5                         (23•55)

Step  5  :

Multiplying exponents :

 5.1    5¹  multiplied by  5³   = 5^{(1 + 3)} = 5⁴

Dividing exponents :

 5.2    2²   divided by   2³   = 2^{(2 - 3)} = 2^(-1) = ¹/_2¹ = ¹/₂

Equation at the end of step  5  :

    9       1   
  ———— ÷ ———————
  1250   (23•55)

Step  6  :

           9          1   
 Divide  ————  by  ———————
         1250      (23•55)

 6.1    Dividing fractions

To divide fractions, write the divison as multiplication by the reciprocal of the divisor :

  9         1            9      (23•55)
————  ÷  ———————   =   ————  •  ———————
1250     (23•55)       1250        1   

Dividing exponents :

 6.2    2³   divided by   2¹   = 2^{(3 - 1)} = 2²

Dividing exponents :

 6.3    5⁵   divided by   5⁴   = 5^{(5 - 4)} = 5¹ = 5

Final result :

  180