In the algebraic expression x^{a}, where x is raised to the power a, x is called a base and a is called an exponent.
Here are the basic rules of exponents, where the bases x and y are nonzero real numbers and the exponents a and b are integers.
Name |
Rule |
Example |
Zero Exponent |
x^{0} = 1 for x ≠ 0 |
5^{0} = 1, (−2)^{0}= 1, 0^{0} is undefined |
Product Rule |
x^{a}x^{b} = x^{a+b} |
x^{2}x^{3} = x^{2+3} = x^{5} |
Quotient Rule |
||
Power Rule |
(x^{a})^{b} = x^{ab} |
(x^{2})^{3} = x^{2×3} = x^{6} |
Negative Exponent |
||
Same Exponent |
(x^{a})(y^{a}) = xy^{a} |
(2^{a})(3^{a}) = 6^{a} |
• (x + y)^{a} ≠x^{a }+ y^{b}
For example, (x + y)^{2} = x^{2} + 2xy + y^{2}
• (−x)^{2} ≠−x^{2}
Instead,
(−x)^{2} = x^{2}
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