each subinterval, and record the sign of the
expression above each:The inequality does not include “equals,” so we
do not include those values from the number
line that make the numerator equal to zero.
The solution set is (–∞, –4).Section 5—Radical
Expressions and Quadratic
EquationsSet 36(Page 90)
- c.–125 since (–5)^3 = –125.
- c.–7 and 7 are both second roots (square
roots) since (–7)^2 = 49 and (7)^2 = 49. - a.Note that 625 = 5^4. So, the principal root of
625 is 5. - d.Since(–2)^5 = –32, we write ^5 –32= –2.
- a.Since 4^3 = 64,b= 64 satisfies the equation.
- a.^43 ^12 = ^4 (3^3 )^4 = 3^3 = 27
- c.^55 ^15 = ^5 (5^3 )^5 = 5^3 = 125
- b.Since ^4 (2b)^4 = 2b,b= 3 satisfies the
equation. - b.64 = (2^6 )= 2
- d.We break up the fractional exponent into
two separate exponents to obtain 49 = (49 )^5
= 7^5 = 16,807. - a.We break up the fractional exponent into
two separate exponents to obtain 81– =
(81 )–3= 3–3= 313 = 217 .- c.We break up the fractional exponent into
two separate exponents to obtain 32 = (32 )^3
= (^532 )^3 = (2)^3 = 8. - c.( 287 )– = (^23 )^3 – = (^23 )–2= (^32 )^2 = ^32
2
2 = ^94 .- a.(–64)– = [(–4)3]– = (–4)–1= –^14 = –^14
- c.(4x–4)– = (2x–2)–2
-
= (2x–2)–1 = 2 x^1 –2=x 2(^2)
576. b. 4 x^144 = 4(x^72 )^2 = 4x^72
Set 37 (Page 91)
- b.^39 ^3 –3= ^3 (9)(–3)= ^3 –27=
^3 (–3)^3 = –3 - b. = = =
2
= ^1 x- a.a^3 a^3 = a^3 a^2 a= a^3 aa= a^4 a
- a.Factor 4 ginto two radicals. 4 is a perfect
square, so factor 4 ginto 4 g= 2g.
Simplify the fraction by dividing the numera-
tor by the and denominator. Cancel the g
terms from the numerator and denominator.
That leaves ^42 = 2. - a.The cube root of 27y^3 = 3y, since (3y)(3y)(3y)
= 27y^3. Factor the denominator into two radi-
cals: 27 y^2 .= 9 y^2 3 . The square root of
9 y^2 = 3y, since (3y)(3y) = 9y^2. The expression
is now equal to. Cancel the 3yterms
from the numeratorand denominator, leaving
. Simplify the fraction by multiplying the
numeratorand denominatorby : 3 :
( )( ) =. - c.Factor each term in the numerator:a^2 b=
a^2 b= aband ab^2 = ab^2 =
ba. Next, multiply the two radicals. Multiply
the coefficients of each radical and multiply
the radicands of each radical: (ab)(ba) =
abab. The expression is now ababab.Cancel
^3
3
^3
3
^1
3 ^1
3 y
3 y 3 ^1
x
^1
x^2
x^5
x^7
x^5
x^7^12 ^12^13 ^13^23 ^23^35 ^15^1
4^34^5 ^12
2^16 ^16–4 –1 1ANSWERS & EXPLANATIONS–