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pg 49­R.6­Rational Exponents
Negative Exponent­
Suppose that a is a nonzero real number and n is any integer.
Evaluate each expression.
1) 2) 3)
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Write the expression without negative exponents. Assume all variables represent nonzero real numbers.
4) 5) CAUTION: A negative exponent indicates a reciprocal, not a sign change of the expression.
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Quotient Rule­
Suppose that m and n are integers and a is a nonzero real number.
CAUTION: When applying the quotient rule, be sure to subtract the exponents in the correct order. Be careful especially when the exponent in the denominator is negative, and avoid sign errors.
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Simplify each expression. Assume all variables represent nonzero real numbers. 6) 7) 8)
9)
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Simplify each expression. Write answers without negative exponents. Assume all variables represent nonzero real numbers.
10) 11) 12) 5
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CAUTION: Notice the use of power rule goes to both factors. Reminder that it goes to coefficient, too.
The expression
If n is an even positive integer, and if a>0, then is the positive real number whose nth power is a. That is,
If n is an odd positive integer, and if a is any noznero real number, then is the positive or negative real number whose nth power is a. That is, 6
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Evaluate each expression.
13) 14) 15) 16) 17) 18) 19) 20) 7
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The expression
Let m be any integer, n be any positive integer, and a be any real number for which is a real number.
21) 22) 23)
24) 25) 8
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26)
Definition and Rules for Exponents
Suppose that r and s represent rational numbers. The results here are valid for all positive numbers a and b. Product Rule
Power Rules
Quotient Rule
Negative Exponent
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Simplify each expression. Assume all variables represent positive real numbers.
27) 28) 29) 30) 31) 10
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Factor out the least power of the variable or variable expression. Assume all variables represent positive real numbers.
32) 33) 34) 11
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