32 = 9. b) y-1 Write the reciprocal of y -1 and change the sign of the exponent. %3D 8 x %3D y 1 C) (-2)-3 Because of the parentheses, the base is -2. Write the reciprocal of (-2)~3 and change the exponent from -3 to 3. %3D (-2) 2x (-2)3 = -8. 16 X (p. 5-2 - 10-2 = Write the reciprocal of 5~2 and 10-2 and change the sign of each exponent. 10 1. Evalute: 52 = 25 and 102 = 100. 27 X 81 x 1 Build 1/25 to have a denominator of 100 so that the fractions can be subtracted: 1/25 = 1/25 · 4/4 = 4/100 %3D 100 100 2x %3D 100

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
ChapterP: Prerequisites
SectionP.4: Rational Exponents And Radicals
Problem 18E
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I need help with b, c and d.

Express using positive exponents and simplify, if possible: (a) 3-2, (b) y-1, (c) (-2)-3, and (d) 5-2 – 10-2
Since each exponent is a negative number, we will use the negative exponent rule.
This rule enables us to write an exponential expression that has a negative exponent in an equivalent form using a positive exponent.
1
(a)
3-2
Write the reciprocal of 32 and change the sign of the exponent.
1
32 =
= 9.
9.
1
(b)
y-1
Write the reciprocal of y
and change the sign of the exponent.
1
1
(c)
(-2)-3
Because of the parentheses, the base is –2. Write the reciprocal of (-2)¯³ and change the exponent from -3 to 3.
(-2)
1
(-2)3 = -8.
16 X
1
1
(d)
5-2 – 10-2 =
Write the reciprocal of 5-2 and 10-2 and change the sign of each exponent.
2
10
1
Evalute: 52 = 25 and 102 = 100.
27X
81X
Build 1/25 to have a denominator of 100 so that the fractions can be subtracted: 1/25 = 1/25 · 4/4 = 4/100
%3D
100
100
100
Transcribed Image Text:Express using positive exponents and simplify, if possible: (a) 3-2, (b) y-1, (c) (-2)-3, and (d) 5-2 – 10-2 Since each exponent is a negative number, we will use the negative exponent rule. This rule enables us to write an exponential expression that has a negative exponent in an equivalent form using a positive exponent. 1 (a) 3-2 Write the reciprocal of 32 and change the sign of the exponent. 1 32 = = 9. 9. 1 (b) y-1 Write the reciprocal of y and change the sign of the exponent. 1 1 (c) (-2)-3 Because of the parentheses, the base is –2. Write the reciprocal of (-2)¯³ and change the exponent from -3 to 3. (-2) 1 (-2)3 = -8. 16 X 1 1 (d) 5-2 – 10-2 = Write the reciprocal of 5-2 and 10-2 and change the sign of each exponent. 2 10 1 Evalute: 52 = 25 and 102 = 100. 27X 81X Build 1/25 to have a denominator of 100 so that the fractions can be subtracted: 1/25 = 1/25 · 4/4 = 4/100 %3D 100 100 100
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