Definitions and Rules for Exponents For all integers m and n and all real numbers a and b, the following rules apply. Product Rule am.an = a m+n Quotient Rule…
Tag: Exponents
Power Rules for Exponents
Power Rules for Exponents If a and b are real numbers and m and n are integers, then (a) (am)n = amn . (b) (ab)m = ambm (c) (a/b)m =…
Quotient Rule for Exponents
Quotient Rule for Exponents If a is any nonzero real number and m and n are integers, then am/an = am-n. In words, when dividing powers of like bases, keep…
Define 0 and negative exponents
Define 0 and negative exponents So far we have discussed only positive exponents. Now we define 0 as an exponent. Suppose we multiply 42by 40. By the product rule,…
Product Rule for Exponents
Product Rule for Exponents If m and n are natural numbers and a is any real number, then am. an = am+n. In words, when multiplying…
Laws of Exponents
Laws of Exponents The same laws hold for rational-number exponents as for integer exponents. We list them for review. For any real number a and any rational exponents m…
Negative Rational Exponents
Negative Rational Exponents Negative rational exponents have a meaning similar to that of negative integer exponents. a-m/n For any rational number m/n and any positive real number a, a-m/n…
Rational Exponents
Rational Exponents Expressions like a1/2 , 5-1/4 ,and (2y)4/5 have not yet been defined. We will define such expressions so that the general properties of exponents hold. Consider a1/2.a1/2. If…
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