UNIVERSITY OF TECHNOLOGY, JAMAICA
SCHOOL OF MATHEMATICS & STATISTICS
COLLEGE MATHEMATICS 1A/B (MAT 1044/1047)
TOPIC: INDICES
WORKSHEET #2
1. Simplify the following:
(i)
( ab )
(a
2
( 3x y )
( 3xy )
2
(v)
)
−1 −1 2
b
(ii) 3n  9n
(iv) 9(a 6  a3 )
(iii) 5a 4 b 3 (a 2 b 5 ) 2
1
2
(vi)
2 −2
9 0  35  81 32 2
(vii)
38  163
x4 ( y 2 z3 )4
(x 2 z −5 )2
(viii)
1
86  43
1
6
32  16
1
12
2. Simplify the following:
1
3
(i) 27 3
(ii) 9 2
 16 
(v)  
 81 
−
1
4
(vi)
(2 )(12 )
(3 )(8 )
n +1
(ix)
n +1
n −1
n −1
(x)
5
(iii) 32
x10
32 y 25
−
3
5
(iv)
(vii) 5n +1  25n  125
(3 )  9
(3 ) (3 )
n +3
n +1
n n −1
n −1 n +1
(xi)
3 n −1
3
(6 )(9 )
(3 )(2 )
2 n +1
2n
5 n +1
2n
(5 5 )10
2
(32 )  
3
(viii)
1
5
16
3
5
(xii)
−2
8 n + 2  6 ( 23 n + 3 )
( 2 )( 4 )
n
n+2
3. Solve the following equations for the unknown:
(i) 4
3n
= 32
(v) 83 x−9 − 12 = 500
(ii) 3
y+4
1
= 
9
(vi) 3  5 x =
y
3
125
(iv) 4  2 6−3n = 32
(iii) 4 3n +6 = 1
(vii) ( 27 x +1 )( 32 x ) =
1
81
( )
1
(viii) 35 x  
9
1− 4 x
= 81x +1
4. Solve the following equations for x:
(i) (22 x ) − 5(2 x ) + 4 = 0
(ii) 4 x − 9(2 x ) + 8 = 0
(iii) ( 22 ) − 6 ( 21 ) + 8 = 0
(iv) 9 x − 12(3x ) + 27 = 0
(v) 2(22 x ) − 5(2 x ) + 2 = 0
(vi)
x
( 4)
x
x
− 10 ( 2 x ) = −16
Reviewed August 2019
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