Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-7" was replaced by "^(-7)".

(2): "7.6" was replaced by "(76/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

    29        76
  ((——•(105))•——)•((2)(-7)•(5)(-7))
    10        10

Step  2  :

            38
 Simplify   ——
            5 

Equation at the end of step  2  :

    29            38
  ((—— • (105)) • ——) • ((2)(-7)•(5)(-7))
    10            5 

Step  3  :

 3.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  3  :

    29              38
  ((—— • (25•55)) • ——) • ((2)(-7)•(5)(-7))
    10              5 

Step  4  :

            29
 Simplify   ——
            10

Equation at the end of step  4  :

    29              38
  ((—— • (25•55)) • ——) • ((2)(-7)•(5)(-7))
    10              5 

Step  5  :

Dividing exponents :

 5.1    2⁵   divided by   2¹   = 2^{(5 - 1)} = 2⁴

Dividing exponents :

 5.2    5⁵   divided by   5¹   = 5^{(5 - 1)} = 5⁴

Equation at the end of step  5  :

                38
  ((29•24•54) • ——) • ((2)(-7)•(5)(-7))
                5 

Step  6  :

Multiplying exponents :

 6.1    2⁴  multiplied by  2¹   = 2^{(4 + 1)} = 2⁵

Dividing exponents :

 6.2    5⁴   divided by   5¹   = 5^{(4 - 1)} = 5³

Equation at the end of step  6  :

  (29•25•53•19) • ((2)(-7)•(5)(-7))

Step  7  :

Dividing exponents :

 7.1    2⁵   divided by   2⁷   = 2^{(5 - 7)} = 2^(-2) = ¹/_2²

Dividing exponents :

 7.2    5³   divided by   5⁷   = 5^{(3 - 7)} = 5^(-4) = ¹/_5⁴

Final result :

   551           
  ———— = 0.22040 
  2500