Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-2" was replaced by "^(-2))". 1 more similar replacement(s)

(2): "7.6" was replaced by "(76/10)". 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  :

   1 76
  (—•——)•((2)(-2)•(5)(-2))
   1 10

Step  2  :

            38
 Simplify   ——
            5 

Equation at the end of step  2  :

   1   38
  (— • ——) • ((2)(-2)•(5)(-2))
   1   5 

Step  3  :

 3.1     10 = 2•5

(10)^-14 = (2•5)^(-14) = (2)^(-14) • (5)^(-14)

Equation at the end of step  3  :

   1   38
  (— • ——) • ((2)(-2)•(5)(-2))
   1   5 

Step  4  :

             1          38
 Divide  —————————  by  ——
         (214•514)       5 

 4.1    Dividing fractions

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

    1         38           1          5
—————————  ÷  ——   =   —————————  •  ——
(214•514)      5        (214•514)      38

Multiplying exponents :

 4.2    2¹⁴  multiplied by  2¹   = 2^{(14 + 1)} = 2¹⁵

Dividing exponents :

 4.3    5¹   divided by   5¹⁴   = 5^{(1 - 14)} = 5^(-13) = ¹/_5¹³

Equation at the end of step  4  :

   1         1     
  (— • ————————————) • ((2)(-2)•(5)(-2))
   1   (215•513•19) 

Step  5  :

            1
 Simplify   —
            1

Equation at the end of step  5  :

             1     
  (1 • ————————————) • ((2)(-2)•(5)(-2))
       (215•513•19) 

Step  6  :

Multiplying exponents :

 6.1    2¹⁵  multiplied by  2²   = 2^{(15 + 2)} = 2¹⁷

Multiplying exponents :

 6.2    5¹³  multiplied by  5²   = 5^{(13 + 2)} = 5¹⁵

Final result :

        1                                        
  ———————————— = 1.31579 • 10-17 
  (217•515•19)