Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-6" was replaced by "^(-6)". 1 more similar replacement(s)

(2): "7.5" was replaced by "(75/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)^-6 = (2•5)^(-6) = (2)^(-6) • (5)^(-6)

Equation at the end of step  1  :

    342         75
  ((———•(10-7))•——)•((2)(-6)•(5)(-6))
    100         10

Step  2  :

            15
 Simplify   ——
            2 

Equation at the end of step  2  :

    342             15
  ((——— • (10-7)) • ——) • ((2)(-6)•(5)(-6))
    100             2 

Step  3  :

 3.1     10 = 2•5

(10)^-7 = (2•5)^(-7) = (2)^(-7) • (5)^(-7)

Equation at the end of step  3  :

    342                        15
  ((——— • ((2)(-7)•(5)(-7))) • ——) • ((2)(-6)•(5)(-6))
    100                        2 

Step  4  :

            171
 Simplify   ———
            50 

Equation at the end of step  4  :

    171                        15
  ((——— • ((2)(-7)•(5)(-7))) • ——) • ((2)(-6)•(5)(-6))
    50                         2 

Step  5  :

Multiplying exponents :

 5.1    2¹  multiplied by  2⁷   = 2^{(1 + 7)} = 2⁸

Multiplying exponents :

 5.2    5²  multiplied by  5⁷   = 5^{(2 + 7)} = 5⁹

Equation at the end of step  5  :

     171     15
  (——————— • ——) • ((2)(-6)•(5)(-6))
   (28•59)   2 

Step  6  :

Multiplying exponents :

 6.1    2⁸  multiplied by  2¹   = 2^{(8 + 1)} = 2⁹

Dividing exponents :

 6.2    5¹   divided by   5⁹   = 5^{(1 - 9)} = 5^(-8) = ¹/_5⁸

Equation at the end of step  6  :

    513  
  ——————— • ((2)(-6)•(5)(-6))
  (29•58)

Step  7  :

Multiplying exponents :

 7.1    2⁹  multiplied by  2⁶   = 2^{(9 + 6)} = 2¹⁵

Multiplying exponents :

 7.2    5⁸  multiplied by  5⁶   = 5^{(8 + 6)} = 5¹⁴

Final result :

     513                                      
  ————————— = 2.56500 • 10-12 
  (215•514)