Section 1.2
Try It!
Section 1.1
1.
Simplify the following.
(a) a10 × a8(b)(5x3y4) × (6xy7)
5.
Evaluate the following.
(a)30 – 3–2
(b)5–9 × 56
(c)(2–9)5 ÷ (26)–7
(d)
Solution
Solution
(a) a10 × a8= a10 + 8
= a18
(a)30 – 3–2= 1 –
(b)(5x3y4) × (6xy7)= (5 × 6)x3 + 1 y4 + 7
= 30x4y11
2.
(b)(30r 9s10) ÷ (6r 8s3)
11
17 – 11
(b)(30r9s10) ÷ (6r8s3)=
3.
Simplify the following.
(a)(b9)5
=
 30  9 – 8 10 – 3
)(s
)
 6  (r
= 5rs
(b)(c6)8 ÷ (c3)10
Solution
(b)(c ) ÷ (c ) = (c ) ÷ (c
= (c48)(c30)
= c48 – 30
= 18
c
4.
3 10
6×8
Simplify the following.
(a)( p2q5)4 × ( p3q)6
Solution
)
3 × 10
(b)
4
÷
 –9 a 3 
 6 
b
(a)( p q ) × ( p q) = ( p q ) × ( p q
= ( p8q20) × ( p18q6)
= ( p18 + 8q20 + 6)
= p26q26
= ( pq)26
2 5 4
4
6
2
3 × 6 1 × 6
 34 a 5 × 4 
 3 × 4 
b
=
 81a 20 
 12 
b
÷
 81a 6 
 12 
b
=
 81a 20 
 12 
b
×
 b 12 

6 
81a 
=
81 20 – 6 12 – 12
(a )(b
)
81
÷
 –9 a 3 
 6 
b
2 × 4 5 × 4
=
(b)
 3a 5 
 3 
b
3
=
=
(d)
6.
 3a 5 
 3 
b
÷
1
3
5
1
125
(c)(2–9)5 ÷ (26)–7= 2–9 × 5 ÷ 26 × (–7)
= 2– 45 ÷ 2– 42
= 2– 45 – (– 42)
= 2–3
7
(a)(b9)5= b9 × 5
= b45
6 8
1
2
3
1
9
(b)5–9 × 56= 5–9 + 6
= 5–3
=
(a) q ÷ q = q
= q6
17
)
 (–9) 2 a 3 × 2 


6×2
b
2
 7
 6 
–1
=
1
23
1
8
6
7
Simplify the following and express your answers in
positive exponential notation.
(a)(m– 4n3)–5
(b)( p6q–2)( p–6q–3)
(c)(5x– 4y8) ÷ (15x–3y6)
Solution
(a)(m– 4n3)–5= m(– 4) × (–5)n3 × (–5)
= m20n–15
=
m 20
n 15
(b)( p6q–2)( p– 6q–3) = p6 + (– 6)q–2 + (–3)
= p0q–5
=
1
q5
( p0 = 1)
(c)(5x y ) ÷ (15x y )=
– 4 8
–3 6
=
=
 5  – 4 – (–3) 8 – 6
)(y )
 15  (x
1 –1 2
(x )(y )
3
y2
3x
= a14
Chapter 1 EXPONENTS
02 DMCC8A_ch1 TryIt(19-21).indd 19
–1
9
Simplifythe following.
(a) q17 ÷ q11
Solution
=1–
8
=
 7
 6 
AND SCIENTIFIC NOTATION
19
9/16/13 1:04 PM