Exponents are subject to many laws, just like other mathematical properties. These are X^1 = X, X^0 = 1, X^-1 = 1/X, X^m * X^n = X^m+n, X^m/X^n = X^m-n, (X^m)^n = X^(m*n), (XY)^n = X^n * Y^n, (X/Y)^n = X^n/Y^n, and X^-n = 1/X^n.
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The laws of exponents work the same with rational exponents, the difference being they use fractions not integers.
the base and the laws of exponent
They are not. Exponents, powers and indices are terms used for the same thing.
That depends how you choose to number the laws.
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