Laws of exponents
SAT glossary · Course Foundations
Definition
x^ax^b=x^a+b, (x^a)/(x^b)=x^a-b, (x^a)^b=x^ab, x^-a=(1)/(x^a), and x^a/b=sqrt[b]x^a. Carried, not provided; the rational-exponent trap is taking only the root or only the power — root first, then power.
Laws of exponents in plain English
These are the core rules for working with exponents (the little raised numbers that mean 'multiply by itself this many times'). When you multiply two powers with the SAME base, you ADD their exponents: x^ax^b=x^a+b. When you divide them, you SUBTRACT: (x^a)/(x^b)=x^a-b. When you raise a power to another power, you MULTIPLY the exponents: (x^a)^b=x^ab. A negative exponent means 'flip it into a fraction': x^-a=(1)/(x^a). And a fractional exponent secretly means a root: x^a/b=sqrt[b]x^a. None of these are handed to you on a reference sheet, so they need to be memorized cold. The most common slip-up with fractional exponents is doing only HALF the job — taking just the root or just the power instead of both; the safe order is root first, then power.
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