Math homework please help?

a)

3.24 x 10^10(5.7 x 10^6) = 18.5 x 10^16 = 1.85 x 10^17

b)

(7.91 x 10^-7)(6.43 x 10^25) = 50.9 x 10^18 = 5.09 x 10^19

c)

(1.873 x 10^5)/(7.64 x 10^-7) = 0.245 x 10^12 = 2.45 x 10^11

d)

(4.73 x 10^-17)/(6.02 x 10^-8) = 0.786 x 10^-9 = 7.86 x 10^-10

e)

(7.46 x 10^9)^2 = 7.46 x 10^18

f)

1/(2.45 x 10^-7) = 2.45 x 10^7

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http://en.wikipedia.org/wiki/Scientific_notation

a = 32.4 billion * 5.7 million → you know that: 1 billion = 1 000 000 000 = 10^9

a = (32.4 * 10^9) * 5.7 million → you know that: 1 million = 1 000 000 = 10^6

a = (32.4 * 10^9) * (5.7 * 10^6)

a = (32.4 * 5.7) * (10^9 * 10^6) → you know that: (x^a) * (x^b) = x^(a + b)

a = (32.4 * 5.7) * 10^(9 + 6)

a = 184.68 * 10^15 ← you can stop here, but you can continue

a = (1.8468 * 100) * 10^15 → you know that: 100 = 10^2

a = (1.8468 * 10^2) * 10^15

a = 1.8468 * (10^2 * 10^15)

a = 1.8468 * 10^(2 + 5)

a = 1.8468 * 10^7

b = 7.91 * 10^(- 7) * 6.43 * 10^25

b = 7.91 * 6.43 * 10^(- 7) * 10^25

b = (7.91 * 6.43) * 10^(- 7 + 25)

b = 50.8613 * 10^18 ← you can stop here, but you can continue

b = (5.08613 * 10) * 10^18

b = 5.08613 * 10^1 * 10^18

b = 5.08613 * 10^(1 + 18)

b = 5.08613 * 10^19

c = (1.873 * 10^5) / [7.64 * 10^(- 7)]

c = (1.873/7.64) * 10^5 / 10^(- 7)

c = (1.873/7.64) * 10^5 * [1/10^(- 7)] → you know that: 1/(x^a) = x^(- a)

c = (1.873/7.64) * 10^5 * 10^7

c = (1.873/7.64) * 10^(5 + 7)

c = (1.873/7.64) * 10^12

c ≈ 0.245157068 * 10^12 ← you can stop here, but you can continue

c ≈ (2.45157068/10) * 10^12

c ≈ [2.45157068 * (1/10)] * 10^12

c ≈ 2.45157068 * 10^(- 1) * 10^12

c ≈ 2.45157068 * 10^(- 1 + 12)

c ≈ 2.45157068 * 10^11

d = [4.73 * 10^(- 17)] / [6.02 * 10^(- 8)]

d = (4.73/6.02) * 10^(- 17) / 10^(- 8)

d = (4.73/6.02) * 10^(- 17) * 10^8

d = (4.73/6.02) * 10^(- 17 + 8)

d = 0.7857142857 * 10^(- 9) ← you can stop here, but you can continue

d = (7.857142857/10) * 10^(- 9)

d ≈ 7.857142857 * 10^(- 1) * 10^(- 9)

d ≈ 7.857142857 * 10^(- 1 - 9)

d ≈ 7.857142857 * 10^(- 10)

e = (7.46 * 10^9)²

e = (7.46 * 7.46) * (10^9 * 10^9)

e = 55.6516 * 10^9 * 10^9

e = 55.6516 * 10^(9 + 9)

e = 55.6516 * 10^18 ← you can stop here, but you can continue

e = (5.56516 * 10) * 10^18

e = 5.56516 * 10^1 * 10^18

e = 5.56516 * 10^19

f = 1/(2.5 * 10^(- 7)]

f = (1/2.5) * [1/10^(- 7)]

f = 0.4 * [1/10^(- 7)]

f = 0.4 * 10^7 ← you can stop here, but you can continue

f = (4/10) * 10^7

f = [4 * 1/10] * 10^7

f = [4 * 1/10^(1)] * 10^7

f = 4 * 10(- 1) * 10^7

f = 4 * 10^(- 1 + 7)

f = 4 * 10^6

a. (32.4 billion)(5.7 billioin) = 184.68 billion ≈ 184.7 billion (rounded).....ANS

b. (7.91 x 10⁻⁷)(6.43 x 10²⁵) = 50.8613 x 10¹⁸ ≈ 5.09 x 10¹⁹ ................ANS

c. 1.873 x 10⁵

....----------------- ≈ 2.45 x 10¹¹.................ANS

....7.64 x 10⁻⁷

d. 4.73 x 10⁻¹⁷

...----------------- ≈ 7.86 x 10⁻¹⁰..................ANS

....6.02 x 10⁻⁸

e. (7.46 x 10⁹)² = 55.7 x 10¹⁸...................ANS

f...........1

...--------------- = 0.4 x 10⁷.........................ANS

...2.5 x 10⁻⁷