EXAMPLE 1 Simplify each expression. Assume that x can represent any nonzero real number. (a) 64-1/2 (b) (-16)-5/4 (c) -625-3/4 (d) (-32x5)-2/5 and (e) 25-3/2 Strategy We will use one of the rules x-m/n = xm/n = xm/n to write the reciprocal of each exponential expression and change the exponent's sign to positive. or Why If we can produce an equivalent expression having a positive rational exponent, we can use the methods of this section to simplify it. Solution Because the exponent is negative, write the reciprocal of 64-1/2, and change the sign of the 64-1/2 = 641/2 (a) exponent. (b) (-16)-5/4 is not a real number because (-16)5/4 is not a real number. (c) In -625-3/4, the base is 1 1 -625-3/4 = - 6253/4 (V525)3 =- 125 (d) (-32x5)-2/5 = (-32-)2/5 = (V-325)² (-292 %3D %3D Because the exponent is negative, write the reciprocal of and change the sign of the (e) -32 = 253/2 = (/ 25)³ = 53 = 25-3/2 exponent.
EXAMPLE 1 Simplify each expression. Assume that x can represent any nonzero real number. (a) 64-1/2 (b) (-16)-5/4 (c) -625-3/4 (d) (-32x5)-2/5 and (e) 25-3/2 Strategy We will use one of the rules x-m/n = xm/n = xm/n to write the reciprocal of each exponential expression and change the exponent's sign to positive. or Why If we can produce an equivalent expression having a positive rational exponent, we can use the methods of this section to simplify it. Solution Because the exponent is negative, write the reciprocal of 64-1/2, and change the sign of the 64-1/2 = 641/2 (a) exponent. (b) (-16)-5/4 is not a real number because (-16)5/4 is not a real number. (c) In -625-3/4, the base is 1 1 -625-3/4 = - 6253/4 (V525)3 =- 125 (d) (-32x5)-2/5 = (-32-)2/5 = (V-325)² (-292 %3D %3D Because the exponent is negative, write the reciprocal of and change the sign of the (e) -32 = 253/2 = (/ 25)³ = 53 = 25-3/2 exponent.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
Transcribed Image Text:EXAMPLE 1 Simplify each expression. Assume that x can represent any nonzero real number.
(a) 64-1/2 (b)
(-16)-5/4 (c)
-625-3/4 (d) (-32x5)-2/5 and (e)
1
25-3/2
Strategy
1
or
x-m/n
We will use one of the rules x-m/n
1
xm/n to write the reciprocal of each exponential expression and change the exponent's sign to positive.
tm/n
Why If we can produce an equivalent expression having a positive rational exponent, we can use the methods of this section to simplify it.
Solution
1
Because the exponent is negative, write the reciprocal of 64¬1/2, and change the sign of the
1
(a)
64-1/2
641/2
64
8.
exponent.
(b) (-16)-5/4
is not a real number because (-16)5/4 is not a real number.
(c) In -625-3/4, the base is
1
1
-625-
-3/4
625)3
1
1
%3D
%3D
%D
6253/4
53
125
1
1
(d)
(-32x5)-2/5 =
1
%D
%D
(-32x5)2/5 ¯ (V-32x5)2
(-2x)²
1
(e) -3/2 = 253/2 = (/25)³ = 53 =
Because the exponent is negative, write the reciprocal of
1
25-3/2
and change the sign of the
25-3/2'
exponent.
||
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