Potenz Rechnung Erklärung?

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2 Antworten

Potenzgesetze →

a ^ n * a ^ m = a ^ (n + m)

a ^ n / a ^ m = a ^ (n - m)

(a ^ n) ^ m = a ^ (n * m) = (a ^ m) ^ n

(a * b) ^ n = a ^ n * b ^ n

(a / b) ^ n = a ^ n / b ^ n für b ≠ 0

a ^ (-n) = 1 / a ^ n

(a ^ n) / (b ^ n) = (a / b ) ^ n

a, b, m und n stehen für Zahlen

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2 ^ 6 = 2 * 2 * 2  * 2 * 2  * 2 = 64

5 ^ 2 = 5 * 5 = 25

2 ^ 6 + 5 ^ 2 = 64 + 25 = 89

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15 ^ 4 * 15 ^ -3 = 15 ^ (4 - 3) = 15 ^ 1 = 15

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2.6 * 10 ^ 11 * 0.08 = 2.6 * 0.08 * 10 ^ 11 = 0.208 * 10 ^ 11 = 2.08 * 10 ^ 10

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(5.1 * 10 ^ 15) / 722 = (5.1 / 722) * 10 ^ 15 = 7.06371191135734 * 10 ^ -3 * 10 ^ 15 = 7.06371191135734 * 10 ^ (15 - 3) = 7.06371191135734 * 10 ^ 12

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4.16 * 10 ^ 8 * 1590 = 4.16 * 1590 * 10 ^ 8 = 6614.4 * 10 ^ 8 = 6.6144 * 10 ^ 3 * 10 ^ 8 = 6.6144 * 10 ^ (3 + 8) = 6.6144 * 10 ^ 11

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(1.5 * 10 ^ 7) / 0.027 = (1.5 / 0.027) * 10 ^ 7 = 55.5555555555 * 10 ^ 7 = 5.55555555555 * 10 ^ 1 * 10 ^ 7 = 5.55555555555 * 10 ^ (1 + 7) = 5.55555555555 * 10 ^ 8

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3.5 * 10 ^ 6 * 6.02 * 10 ^ 3 = 3.5 * 6.02 * 10 ^ 3 * 10 ^ 6 = 21.07 * 10 ^ 3 * 10 ^ 6 = 2.107 * 10 ^ 1 * 10 ^ 3 * 10 ^ 6 = 2.107 * 10 ^ (1 + 3 + 6) = 2.107 * 10 ^ 10

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(9.4 * 10 ^ 5 * 1.2 * 10 ^ 3) / (6.6 * 10 ^ 7) = ((1.2 * 9.4) / 6.6) * (10 ^ 3 * 10 ^ 5) / 10 ^ 7 = 1.709090909 * 10 ^ 8 / 10 ^ 7 = 1.709090909 * 10 ^ (8 - 7) = 1.709090909 * 10 ^ 1 = 17.09090909
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