For all Real numbers x and y, and for all integers m and n (unless otherwise stated):
Exponent Rule:
Symbolism:
In plain English ...
Zero Exponent
x0 = 1
All numbers (not zero) raised to the zero power equal one.
Negative Exponent
A negative exponent tells you that the factor is on the wrong side of the fraction bar. ( x not zero, n positive).
Product Rule
When multiplying, and the bases are the same, ADD the exponents.
Quotient Rule
When dividing, and the bases are the same, SUBTRACT the exponents, top exponent subtract bottom exponent.
(x not zero)
Power to a Power
When raising a power to a power, MULTIPLY the exponents.
Product to a Power
When raising a product to a power, EACH factor gets raised to the new power.
Quotient to a Power
When raising a quotient to a power, BOTH top and bottom get raised to the new power. (y not zero)
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Exponent Rules:
