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

User Avsej
by
8.0k points

2 Answers

5 votes

Answer

0.32

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)

User Jared Hoberock
by
8.3k points
3 votes

Answer:

0.32

Explanation:

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

User Endemic
by
8.0k points

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