A2400 ch1f Example 9 Chapter 1 Simplifying indices · 2021. 8. 10. · Title: Microsoft Word -...
3
A2400 ch1f | Version 1.1 | September 2020 Simplifying indices A LEVEL LINKS Scheme of work: 1a. Algebraic expressions – basic algebraic manipulation, indices and surds Key points • a m × a n = a m + n • • (a m ) n = a mn • a 0 = 1 • i.e. the nth root of a • • • The square root of a number produces two solutions, e.g. . Example 1 Simplify = 3x 3 6 ÷ 2 = 3 and use the rule to give Example 2 Simplify = x 8 − 4 = x 4 1 Use the rule 2 Use the rule Example 3 Write as a single power of x m mn n a a a - = 1 n n a a = ( ) m m n m n n a a a = = 1 m m a a - = 16 4 =± 5 2 6 2 x x 5 2 6 2 x x m m n n a a a - = 5 5 2 3 2 x x x x - = = 3 5 4 x x x ´ 3 5 35 8 4 4 4 x x x x x x x + ´ = = m n m n a a a + ´ = m m n n a a a - = 1 3x
Transcript of A2400 ch1f Example 9 Chapter 1 Simplifying indices · 2021. 8. 10. · Title: Microsoft Word -...
A2400 ch1f | Version 1.1 | September 2020
Simplifying indices
A LEVEL LINKS Scheme of work: 1a. Algebraic expressions – basic algebraic manipulation, indices and surds
Key points • am × an = am + n
•
• (am)n = amn • a0 = 1
• i.e. the nth root of a
•
•
• The square root of a number produces two solutions, e.g. .
Example 1 Simplify
= 3x3 6 ÷ 2 = 3 and use the rule to
give
Example 2 Simplify
= x8 − 4 = x4
1 Use the rule
2 Use the rule
Example 3 Write as a single power of x
mm n
n
a aa
-=
1nna a=
( )m mn m nna a a= =
1mmaa
- =
16 4= ±
5
262xx
5
262xx
mm n
na aa
-=
55 2 3
2x x xx
-= =
3 5
4x xx´
3 5 3 5 8
4 4 4x x x xx x x
+´= = m n m na a a +´ =
mm n
na aa
-=
13x
A2400 ch1f | Version 1.1 | September 2020
Use the rule , note that the
fraction remains unchanged
Example 4 Write as a single power of x
1 Use the rule
2 Use the rule
Practice questions
1 Simplify.
a b
c d
e f
g h
2 Write the following as a single power of x.
a b c
d e f
3 Write the following without negative or fractional powers.
a b x0 c
d e f
11 13 3
xx
-= 1 mm aa
-=
13
4x
12
12
4 4
4
x x
x-
=
=
1nna a=
1 mm aa
-=
2 3
232x xx´ 5
2102x
x x´3
33 22x xx´ 3 2
5714x yx y
12
2yy y´
12
322
cc c´
( )32
0
2
4
x
x
312 2
2 3x xx x-
´´
1x 7
1x
4 x
5 2x3
1x 3 2
1
x
3x-15x
25x
12x
-34x
-
Watch out!
Remember that any value raised to the power of zero is 1. This is the rule a
0 = 1.
A2400 ch1f | Version 1.1 | September 2020
Answers
1 a b 5x2
c 3x d
e f c–3
g 2x6 h x
2 a x–1 b x–7 c
d e f
3 a b 1 c
d e f
332x
22yx
12y
14x
25x
13x
-23x
-
31x
5 x
5 2x 1x 4 3
1
x
