Exponents (Grade 12 NSC Matric Mathematics): Flashcards

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Exponents
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Base in exponent notation

Number that gets multiplied repeatedly

Exponent in notation

Shows how many times to multiply the base by itself

Multiply same base: am×an=a^m × a^n =

a(m+n)a^{(m+n)}

Divide same base: am÷an=a^m ÷ a^n =

a(m−n)a^{(m-n)}

Power of a power: (am)n=(a^m)^n =

a(m×n)a^{(m×n)}

Power of a product: (ab)n=(ab)^n =

an×bna^n × b^n

Any base to power zero: a0=a^0 =

11 (where a≠0a ≠ 0)

Negative exponent: a−n=a^{-n} =

1an\frac{1}{a^n} (where a≠0a ≠ 0)

Fractional exponent: amn=a^{\frac{m}{n}} =

amn\sqrt[n]{a^m} or (an)m(\sqrt[n]{a})^m

Distributing exponents over addition (a+b)m(a+b)^m

Cannot be done: (a+b)m≠am+bm(a+b)^m ≠ a^m + b^m

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