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Dubai

Power Rules

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Published in: Mathematics
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A quick summary of all the power rules that you'll ever need in any mathematics course written in a clear way for easy memorization and understanding.

Maged / Abu Dhabi

15 years of teaching experience

Qualification: B.Sc. in Mathematics

Teaches: Mental Maths, Vedic Maths, Statistics, Maths, Advanced Maths, Mathematics, GRE, SAT, ACT, EMSAT, IB Exam Preparation, Exam Preparation, Computer

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  1. Introduction to Powers (=exponents) & Power Rules 1) Powers When a number is to be multiplied by itself a power, or an exponent can be used to write this compactly. A positive power or exponent Of a number or variable indicates a product, and the positive integer is the number Of times that the number or variable is a factor in the product. For example, X means (x)(x)(x)(x)(x); that S, x is a factor in the product 5 times. x here is called the base and 5 is called the power (or exponent). involvinq powers: a a an am. bm = (ab)m a Remember: ao = 1 & al = a 2) Meaninq Of neqative integer exponents and rational exponents By definition, raising a nonzero number to the —l power produces its reciprocal: 1 a One also defines 1 a an for any nonzero a and any positive integer n. Raising O to a negative power would imply division by 0, so it a-n+n = 1, is left undefined. a Note that: a where ao is defined above, and this motivates the definition = -7 shown above. So far we've looked at fractional exponents only where the top number was l. How do you interpret x 2/3, for instance? Can you see how to use the power rule?
  2. Since 2/3 = (2)(1/3), you can rewrite x This is the general rule: = (x2)l/3, which is It works the other way, too: 2/3 = When a power and a root are involved, the top part of the fractional exponent is the power and the bottom part is the root. Suppose p and r are the same? Then you have, for instance, But that's the same as e E, and 5/5=1, so it's the same as xl or just x.

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