Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

Step  1  :

 1.1     8 = 23

(8)⁵ = (2³)⁵ = 2¹⁵

Equation at the end of step  1  :

              -3  
  ((63)•10)•—————— ÷ 215
            (12-1)

Step  2  :

 2.1     12 = 22•3

(12)^-1 = (2²•3)^(-1) = (2)^(-2) • (3)^(-1)

Equation at the end of step  2  :

                        -3       
  ((63) • 10) • ————————————————— ÷ 215
                ((2)(-2)•(3)(-1)) 

Step  3  :

                    1  
 Divide  -3  by  ——————
                 (22•3)

Multiplying exponents :

 3.1    3¹  multiplied by  3¹   = 3^{(1 + 1)} = 3²

Equation at the end of step  3  :

                ( -32•22)
  ((63) • 10) • —————————
                   215   

Step  4  :

            ( -32•22)
 Simplify   —————————
               215   

Raising to a Power :

 4.1    2²   divided by   2¹⁵   = 2^{(2 - 15)} = 2^(-13) = ¹/_2¹³

Equation at the end of step  4  :

                 -9 
  ((63) • 10) • ————
                8192

Step  5  :

 5.1     6 = 2•3

(6)³ = (2•3)³ = 2³ • 3³

Equation at the end of step  5  :

                    -9 
  ((23•33) • 10) • ————
                   8192

Step  6  :

Multiplying exponents :

 6.1    2³  multiplied by  2¹   = 2^{(3 + 1)} = 2⁴

Equation at the end of step  6  :

               -9 
  (24•33•5) • ————
              8192

Step  7  :

Multiplying exponents :

 7.1    3³  multiplied by  3²   = 3^{(3 + 2)} = 3⁵

Dividing exponents :

 7.2    2⁴   divided by   2¹³   = 2^{(4 - 13)} = 2^(-9) = ¹/_2⁹

Final result :

  -1215            
  ————— = -2.37305 
   512