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Marat540 [252]
3 years ago
6

What is the simplified form of 0.2 to the fifth power?

Mathematics
2 answers:
anzhelika [568]3 years ago
7 0

Answer

0.32

Step-by-step explanation:

"0.2222" was replaced by "(2222/10000)". 4 more similar replacement(s)

                  1111

Simplify   ————

                  5000

       22            222        2              1111

 (((———•4)•{————}3——)•5)•(————2)

      100           1000      10            5000

1111 = 11•101

(1111)2 = (11•101)2 = 112 • 1012  2.2     5000 = 23•54 (5000)2 = (23•54)2 = 26 • 58

22    ( 222   2     (112•1012)

 (((———•4)•{————}3——)•5)•——————————

    100     1000  10      (26•58)  

           1

Simplify   —

           5

     22    ( 222  1     (112•1012)

 (((———•4)•{————}3—)•5)•——————————

    100     1000  5      (26•58)  

           111

Simplify   ———

           500

     22    111  1     (112•1012)

 (((———•4)•———3)—)•5)•——————————

    100    500  5      (26•58)  

5.1     111 = 3•37

(111)3 = (3•37)3 = 33 • 373  5.2     500 = 22•53 (500)3 = (22•53)3 = 26 • 59

     22    (33•373)   1     (112•1012)

 (((———•4)•———————— ÷ —)•5)•——————————

    100    (26•59)    5      (26•58)  

        (33•373)      1

Divide  ————————  by  —

        (26•59)       5

6.1    Dividing fractions

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

(33•373)     1       (33•373)     5

————————  ÷  —   =   ————————  •  —

(26•59)      5       (26•59)      1

Dividing exponents:

6.2    51   divided by   59   = 5(1 - 9) = 5(-8) = 1/58

     22        (33•373)         (112•1012)

 (((——— • 4) • ————————) • 5) • ——————————

    100        (26•58)           (26•58)  

           11

Simplify   ——

           50

    11        (33•373)         (112•1012)

 (((—— • 4) • ————————) • 5) • ——————————

    50        (26•58)           (26•58)  

Multiplying exponents

8.1    52  multiplied by  58   = 5(2 + 8) = 510

Dividing exponents:

8.2    21   divided by   26   = 2(1 - 6) = 2(-5) = 1/25

Equation at the end of step

8

:

  (11•33•373)        (112•1012)

 (——————————— • 5) • ——————————

   (510•25)           (26•58)  

Dividing exponents

9.1    51   divided by   510   = 5(1 - 10) = 5(-9) = 1/59

 (11•33•373)   (112•1012)

 ——————————— • ——————————

   (59•25)      (26•58)  

Multiplying exponents

10.1    111  multiplied by  112   = 11(1 + 2) = 113

Multiplying exponents:

10.2    59  multiplied by  58   = 5(9 + 8) = 517

Multiplying exponents:

10.3    25  multiplied by  26   = 2(5 + 6) = 211

Final result :

 (113•33•373•1012)          

 ————————— = 0.32

     (517•211)              

Tanya [424]3 years ago
3 0

Answer:

0.32

Step-by-step explanation:

0.2 to the fifth power is 0.00032, so that simplified is 0.32.

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