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Mathematics for IGCSE & O level - Indices 2 (Section 3)

1
Simplify ( rac{x^6}{x^3} ).
Answer
(B)
(x^3)
2
Simplify ( x^4 / x^{-2} ).
Answer
(B)
(x^6)
3
What is the result of ( a^0 )?
Answer
(B)
1
4
Which expression is equal to ( rac{x^{-3}}{x^{-5}} )?
Answer
(B)
(x^2)
5
Simplify ( 9^{ rac{1}{2}} ).
Answer
(A)
3
6
Solve: ( 2^x = rac{1}{8} ).
Answer
(A)
-3
7
Select the expressions that are equivalent to ( rac{1}{a^2}). (Select all that apply)
Answer
A
C
8
Which expression is equivalent to (2^{-3})?
Answer
(B)
( rac{1}{8})
9
Simplify ( a^3 * a^4 ).
Answer
(A)
(a^7)
10
Simplify ( rac{a^5 b^3}{a^2 b} ).
Answer
(A)
(a^3 b^2)
11
Simplify ( (x^2 y^3)^2 ).
Answer
(A)
(x^4 y^6)
12
Simplify ( 2x^3 * 3x^2 ).
Answer
(A)
(6x^5)
13
Select the expressions that simplify to (x^4) (Select all that apply)
Answer
A
B
C
D
14
Which of the following is equivalent to (a^m imes a^n)?
Answer
(B)
(a^{m+n})
15
Which expressions are equivalent to ( rac{1}{9} )? (Select all that apply)
Answer
A
B
16
If (x = 2), what is the value of (x^{-2})?
Answer
(B)
( rac{1}{4})
17
What is the result of ( rac{a^m}{a^m} )?
Answer
(B)
1
18
What is the result of ( a^n / a^n )?
Answer
(B)
1
19
What is ( (x^3)^0 )?
Answer
(B)
1
20
Simplify ( (2x^4)^3 ).
Answer
(D)
(8x^{12})
21
What is the simplified form of ( rac{a^5 b^2}{a^3 b^1})?
Answer
(A)
(a^2b)
22
What is ( sqrt{a^2 b^4} )?
Answer
(A)
(ab^2)
23
Which is equal to ( (2^3)^2 )?
Answer
(C)
64
24
Which expression is equivalent to ( rac{5^2}{5^4})?
Answer
(B)
(5^{-2})
25
Solve for *x*: ( 3^x = 81 ).
Answer
(C)
4
26
Simplify ( (3^2)^2 ).
Answer
(C)
81
27
Find the value of *x*: (9^x = 81).
Answer
(B)
2
28
Which of the following is/are equivalent to (a^5 * a^{-2})? (Select all that apply)
Answer
A
B
29
Which is the simplified form of ( sqrt{x^8} )?
Answer
(A)
(x^4)
30
Choose the correct simplification of (3x^2 + 2x^2). (Select all that apply)
Answer
A
C
31
Which value is equivalent to (( rac{3}{4})^{-1})?
Answer
(B)
( rac{4}{3})
32
Which expression is equal to ( sqrt[4]{x^8} )?
Answer
(B)
(x^4)
33
Which expression is equivalent to ( sqrt[3]{x^6} )?
Answer
(A)
(x^2)
34
Which of the following is equivalent to ( ( rac{1}{2})^{-1} )? (Select all that apply)
Answer
A
D
35
Simplify ( 5x^3 - 2x^3 ).
Answer
(A)
(3x^3)
36
Simplify ( rac{x^5}{x^2} ).
Answer
(A)
(x^3)
37
Which of the following are true? (Select all that apply)
Answer
A
B
D
38
What is the value of ( 5^{-2} )?
Answer
(B)
( rac{1}{25})
39
Simplify ( a^6 / a^{-2} ).
Answer
(C)
(a^8)
40
Which is equal to ( sqrt{16} )?
Answer
(A)
4
41
Solve for *x*: ( 2^x = 32 ).
Answer
(C)
5
42
Simplify ( 4x^2 + 3x^2 ).
Answer
(A)
(7x^2)
43
Simplify ( (x^{-2}y^3)^3 ).
Answer
(A)
(x^{-6}y^9)
44
Which of the following is/are equivalent to ((a^m)^n)? (Select all that apply)
Answer
(A)
(a^{mn})
45
Which expressions are equivalent to (16)? (Select all that apply)
Answer
A
B
46
Simplify ( a^3 imes b^2 imes a^2 ).
Answer
(A)
(a^5b^2)
47
Simplify: ( rac{a^2 * a^4}{a^3} ).
Answer
(A)
(a^3)
48
Simplify ( a^4 imes a^{-2} ).
Answer
(B)
(a^2)
49
Choose the simplified expression for ( rac{x^a * x^b}{x^c}). (Select all that apply)
Answer
A
C
50
Simplify: ( (a^2)^3 )
Answer
(B)
(a^6)