MATHEMATICS-ALGEBRA (Laws)

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Exponents rules and properties Rule name RuleExample

Product rules a n · a m = a n+m

Quotient rules a n / a m = a n-m

Power rules (bn)m = bn·m

Negative exponents b-n = 1 / bn2-3 = 1/23 = 0.125

Zero rules b0 = 150 = 10n = 0 , for n>005 = 0

One rulesb1 b51 = 51n = 115 = 1

Minus one rule (-1)5 = -1

Derivative rule (xn)' = n·x n-1(x3)' = 3·x3-1

Integral rule∫ xndx = xn+1/(n+1)+C∫ x2dx = x2+1/(2+1)+C

Exponents product rules Product rule with same base an · am = an+m

Example:

23 · 24 = 23+4 = 27 = 2·2·2·2·2·2·2 = 128

Product rule with same exponent an · bn = (a · b)n

Example:

32 · 42 = (3·4)2 = 122 = 12·12 = 144

See: Multplying exponents

Exponents quotient rules Quotient rule with same base an / am = an-m

Example:

25 / 23 = 25-3 = 22 = 2·2 = 4

Quotient rule with same exponent an / bn = (a / b)n

Example:

43 / 23 = (4/2)3 = 23 = 2·2·2 = 8

Exponents power rules Power rule I (an) m = a n·m

Example:

(23)2 = 23·2 = 26 = 2·2·2·2·2·2 = 64

Power rule II a nm = a (nm)

Example:

232 = 2(32) = 2(3·3) = 29 = 2·2·2·2·2·2·2·2·2 = 512

Power rule with radicals m√(a n) = a n/m

Example:

2√(26) = 26/2 = 23 = 2·2·2 = 8

Negative exponents rule b-n = 1 / bn

Example:

2-3 = 1/23 = 1/(2·2·2) = 1/8 = 0.125