Algebra and General Mathematics: Laws of Exponents

LAWS OF EXPONENTS

1. Product Rule

x^m · xⁿ = m^{(x + n)}

2. Quotient Rule

x^m / xⁿ = m^{(x – n)}

(x/y)^m = x^m / y^m

3. Power Rule

(x^m)ⁿ = x^mn

(xy)^m = x^my^m

4. Negative Exponent Rule

x^-n = 1 / xⁿ , x ≠ 0

5. Expanded Power Rule

(ax)^m / (by)ⁿ = (a^mx^m) / (bⁿyⁿ)

[ (x^m)ⁿ ]^p = x^mnp

x^(m/n) = ⁿ√x^m

(ⁿ√x) (ⁿ√y) = ⁿ√(xy)

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