Page 103 - Mathematics_Form_Two

Exponents and radicals

Exercise 5�4 3. Write the reciprocals of each of the
1. Simplify each of the following following numbers in simplest form.
expressions and write the answer in (a) 14
positive or zero exponent:
x 4 1
(a) (b)
FOR ONLINE READING ONLY
x 7 8
4
( 3xy 2 ) 3 (c) 100
6
(b)
2
9xy 4 4
( 2xy− 7 4 ) 1 2 (d) t Mathematics for Secondary Schools
(c) 1
3 15
4xy (e) 2 t
88
( 2uv ) 4
3 2
(d) 2 (f) π
4
−
2
( 4uv )
2
−
1
( 5ab ) ( 3a b ) 3 (g) 0.125
23
×
(e) 13
(15ab 2 ) 2 (h) 29
2
23
4
×
( 6mn − 2 ) ( 3m n ) 3
−
(f) 2 (i) 0.25
(18mn − 1 )
(j) 0.75
2. Simplify each of the following
expressions and write the answer in
negative exponent: Exponential equations
3
2 × 4 4 All mathematical equations which
(a)
( ) 2 involve exponents are called exponential
5
2
p
q
3
−
−
1
2
(b) ( x y z 1 )( x yz 4 )( x y ) equations. For example, x = y is an
2 −
exponential equation where x and y are
3 rπ 22 h 4 bases and p and q are exponents. The
(c) laws of exponents are usually used when
π r 3 h solving equations that involve exponents.
3
−
5 −
32
×
( 2a b 3 ) ( 4a b ) 4
(d) The following rules should be considered
4 −
(8ab 2 ) 3 when solving exponential equations:
3
−
(12 ba 3 − 4 ) ( 4ab× − 2 8 ) 3 (a) If the bases are the same, then equate
(e) the exponents. That is, if m = m ,
x
y
( 48a b 2 ) 2 then x = y.
6 −
4
( 6mn − 2 ) 2 (b) If the exponents are equal then
(f)
2
n
n
( 3mn − 4 ) 3 equate the bases. That is, if a = b ,
then a = b.
97
Student's Book Form Two
11/10/2024 20:12:20
MATHEMATIC F2 v5.indd 97
MATHEMATIC F2 v5.indd 97 11/10/2024 20:12:20