When are the Laws of Exponents correct?

Provided $a,b>0$, all the rules are true for real $a,b,m,n$.

If $a=0$ or $b=0$, no negative power may appear.

For $a<0$ or $b<0$, irrational exponents are excluded. Rational ones are possible provided the denominator of the simplified fraction is odd. This can cause rule 5 to fail ($(-1)^1\ne((-1)^{1/2})^2$).


Whenever the base is positive and the exponent is real, or the base is zero and the exponent is positive, or the base is negative and the exponent is an integer.

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Algebra Precalculus

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