Page 24 - 新思维数学活动用书9 样章

2.3 Expressions and indices

11 Which answer is correct, A, B, C or D?
6
a Simplify 3x 9 A 4x B 4x C 1 x D 1 x 3
3
6
12x 3 4 4
.
b Simplify 3y 6 A 1 y B 1 y C 5y D 5y 2
15
2
15
.
15y 4 5 5
c Simplify 30z 10 A 6 z B 6 z C 5 z D 5 k 5
2
5
2
25z 5 5 5 6 6
1
d Simplify 10w 8 A 2 w B 2 C 2 w D 2 1
4w 8 5 5 2 2
Challenge
12 Fill in the missing indices in these fractions. The first one has been done for you.
−
−
3
5
a 4 − 4 = 1 b 5 = 1 c 8 = 1
4 4
5 8
d x = 1 e y = 1 f z = 1
−1
−7
−4
x y z
13 Simplify these expressions. Write each expression as a negative power and as a fraction. The first
one has been started for you.
a x 5 = x 58 = x = 1 b y 3 c m 2 d n
−
3
−
x 8 y 7 m 10 n 6
x
14 Here are six rectangular cards and seven oval cards.
The expressions on the rectangular cards have been simplified to give the expressions on the
oval cards.
7y
A 10y ÷ 15y 8 B 12y ÷ 16y 7 C 20y ÷ 12y 10 D 12y 10 6 E 21y 6 F 24y 9 4
4
3
4
8y
9y
i 5 ii 1 iii 3 iv 3 v 2 vi 5 vii 4
3y 6 3y 5 4y 4 y 5 3y 4 2y 7 3y 4

a Match each rectangular card with the correct oval card.
b There is one oval card left. Write an expression that simplifies

to give the expression on this card. Tip
2
3n
15 Show that the expression 2n × 3n 5 simplifies to . For Question 15,
23
( 2n ) 4 simplify the
4
6
2
16 Do the expressions 6x × 3x × 2x 9 and 3x ( ) 4 simplify to give the numerator, then
2
×
4x 13 3xx × 3x 9 the denominator,
same expression?
Show your working. then combine
your two
expressions.

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