Mathematical formulas

Algebra

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1Numbers and algebraic properties
2Powers, exponents, and radicals
3Algebraic expressions
4Notable products and identities
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10Functions
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21Orthogonality and projections
22Least squares
23Matrix decompositions
24Matrix norms and conditioning
25Boolean algebra
26Modular arithmetic
27Algebraic structures
28Linear codes and error correction
29Relationship maps

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Algebra
Powers, exponents, and radicals
Zero and negative exponents

2. Powers, exponents, and radicals

Zero and negative exponents

Level: fundamental

In 2. Powers, exponents, and radicals

Formula

a^0=1;\quad a^{-n}=\frac1{a^n}\;(a\ne0)

Tags

algebra
algebra formula
powers
powers and radicals

Detail

Extends the laws of exponents to zero and negative integers.

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Quotient of powers
$\frac{a^m}{a^n}=a^{m-n}\;(a\ne0)$
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Rational exponent
$a^{m/n}=\sqrt[n]{a^m}$
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