Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-2" was replaced by "^(-2)".

(2): "1.7" was replaced by "(17/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

   51       17
  (——•(106))——•((2)(-2)•(5)(-2)))
   10(      10

Step  2  :

            17
 Simplify   ——
            10

Equation at the end of step  2  :

   51             17
  (—— • (106)) ÷ (—— • ((2)(-2)•(5)(-2)))
   10             10

Step  3  :

Multiplying exponents :

 3.1    2¹  multiplied by  2²   = 2^{(1 + 2)} = 2³

Raising to a Power :

 3.2    5¹  multiplied by  5²   = 5^{(1 + 2)} = 5³

Equation at the end of step  3  :

   51             17 
  (—— • (106)) ÷ ————
   10            1000

Step  4  :

 4.1     10 = 2•5

(10)⁶ = (2•5)⁶ = 2⁶ • 5⁶

Equation at the end of step  4  :

   51               17 
  (—— • (26•56)) ÷ ————
   10              1000

Step  5  :

            51
 Simplify   ——
            10

Equation at the end of step  5  :

  51               17 
  —— • (26•56)) ÷ ————
  10              1000

Step  6  :

Dividing exponents :

 6.1    2⁶   divided by   2¹   = 2^{(6 - 1)} = 2⁵

Dividing exponents :

 6.2    5⁶   divided by   5¹   = 5^{(6 - 1)} = 5⁵

Equation at the end of step  6  :

  )17 
  ————
  1000

Step  7  :

                            17 
 Divide  (3•17•25•55)  by  ————
                           1000

Multiplying exponents :

 7.1    2⁵  multiplied by  2³   = 2^{(5 + 3)} = 2⁸

Multiplying exponents :

 7.2    5⁵  multiplied by  5³   = 5^{(5 + 3)} = 5⁸

Canceling Out :

 7.3      Canceling out  17  as it appears on both sides of the fraction line

Final result :

  (3•28•58)