Mathematics - Exponents and Powers
Exam Duration: 45 Mins Total Questions : 30
What is the value of (30-40) x 52?
- (a)
25
- (b)
0
- (c)
-25
- (d)
1
What is the value of (12 x 3°- 8 x 50)?
- (a)
\(\frac { 1 }{ 2 } \).
- (b)
2
- (c)
4
- (d)
\(\frac { 1 }{ 4 } \).
Find the value of 2° + 3° + 4°.
- (a)
3
- (b)
234
- (c)
1
- (d)
24
Which of the following is the least?
(-1)3, (-10)3, (1)5 and (-1)4
- (a)
15
- (b)
(-10)3
- (c)
(-1)4
- (d)
(-1)3
Write a x a x a x c x c x c x c x d x d in exponential form.
- (a)
a3c3d
- (b)
a3c3d
- (c)
a3c3d2
- (d)
a3c4d2
(-11)2 x (-11)4 =(-11 )x. What is the value of x?
- (a)
2
- (b)
4
- (c)
6
- (d)
-2
What is the value of \(\left[ \left( \frac { 1 }{ 4 } \right) ^{ 2 }-\left( \frac { 1 }{ 4 } \right) ^{ 3 } \right] \times { 2 }^{ 6 }\).
- (a)
1
- (b)
2
- (c)
3
- (d)
4
Expres \(\frac { 729\times 64 }{ 270 } \) as a product of prime factors in exponential form.
- (a)
25 x 34
- (b)
\(\frac { { 2 }^{ 5 }\times { 3 }^{ 3 } }{ 5 } \).
- (c)
\(\frac { { 2 }^{ 5 }\times { 3 }^{ 3 } }{ { 5 }^{ 3 } } \).
- (d)
\(\frac { { 2 }^{ 6 }\times { 3 }^{ 2 } }{ { 5 }^{ 2 } } \).
How is 65950 expressed in standard form?
- (a)
6.59 x 106
- (b)
6.595 x 105
- (c)
6.595 x 104
- (d)
6.59 x 105
Simplify \(\frac { (9m^{ 2 })^{ \frac { 1 }{ 3 } } }{ 6^{ 4 } } \times \frac { (4n^{ 2 })^{ \frac { 1 }{ 3 } } }{ 5m } \) .
- (a)
\(\frac { 1 }{ 5 } \left[ \frac { { n }^{ 2 } }{ m6^{ 10 } } \right] ^{ \frac { 1 }{ 3 } }\).
- (b)
\(\frac { 1 }{ 5 } \left[ \frac { { n } }{ m^{ 2 }6^{ 10 } } \right] ^{ \frac { 1 }{ 3 } }\).
- (c)
\(\frac { 1 }{ 5 } \left[ \frac { { n }^{ 2 } }{ m6^{ -10 } } \right] ^{ \frac { 1 }{ 3 } }\).
- (d)
\(\frac { 1 }{ 5 } \left[ \frac { { n }^{ 2 } }{ m6^{ 10 } } \right] ^{ \frac { 2 }{ 3 } }\).
Simplify and leave the answer in exponent form.
\(\left( \frac { 6 }{ 7 } \right) ^{ -2 }\times \left( \frac { 7 }{ 6 } \right) ^{ -2 }\).
- (a)
\(\frac { 7 }{ 6 } \).
- (b)
1
- (c)
\(\frac { -6 }{ 7 } \).
- (d)
\(\frac { 6 }{ 7 } \).
Simplify \(\frac { { p }^{ 4 }{ q }^{ 3 }\times { p }^{ 2 }{ r }^{ 4 }\times { q }^{ -2 }{ r }^{ 3 } }{ { p }^{ -3 }{ q }^{ 3 }{ r }^{ 3 } } \).
- (a)
p3q4r7
- (b)
p3q4r10
- (c)
p-9q2r-4
- (d)
p9q-2r4
Simplify \(\frac { ({ a }^{ -n })^{ m }\times { a }^{ -2m } }{ a^{ mn }\times { a }^{ 2m } } \).
- (a)
a2m(n-2)
- (b)
a2m(2n-4)
- (c)
a-2m(n+2)
- (d)
a2m(n-4)
Simplify\(\frac { (16a^{ 2 })^{ \frac { 1 }{ 2 } }\times (36{ a }^{ 4 })^{ \frac { -1 }{ 2 } } }{ 2a^{ \frac { 1 }{ 2 } }\times 5a^{ \frac { 3 }{ 2 } }\times 8a^{ \frac { 9 }{ 4 } } } \).
- (a)
120\(a^{ \frac { 25 }{ 4 } }\).
- (b)
\(\frac { 1 }{ 120a^{ \frac { 25 }{ 4 } } } \).
- (c)
24\({ a }^{ \frac { -25 }{ 4 } }\).
- (d)
24\({ a }^{ \frac { 25 }{ 4 } }\).
Solve 92x = 729.
- (a)
x=\(\frac { 3 }{ 4 } \) .
- (b)
x=\(\frac { 2 }{ 3 } \) .
- (c)
x=\(\frac { 5 }{ 6 } \).
- (d)
x=\(\frac { 3 }{ 2 } \) .
Find the value of x.
(53)x x (58)x = 572
- (a)
x=6\(\frac { 6 }{ 11 } \).
- (b)
x=9
- (c)
x=6
- (d)
x=8
Simplify \(\frac { ab^{ 2 }c^{ 3 }\times { a }^{ 4 }{ b }^{ 5 }{ c }^{ -6 } }{ { a }^{ -7 }{ b }^{ -8 }{ c }^{ 9 }\times { a }^{ 10 }{ b }^{ 11 }{ c }^{ -12 }\times { a }^{ 13 }{ b }^{ -14 }{ c }^{ 15 } } \).
- (a)
a11b18c-15
- (b)
a11b18c15
- (c)
a-11b-18c15
- (d)
a-11b18c-15
The speed of light in vacuum is 300, 000, 000 ms-1. Express it in standard
form.
- (a)
3.0 x 108 ms-1
- (b)
3.0 x 1010 ms-1
- (c)
3.0 x 106 ms-1
- (d)
3.0 x 1012 ms-1
23+23+23+23 is equal to____
- (a)
25
- (b)
212
- (c)
281
- (d)
216
The value of\(\frac { \left( -\frac { 1 }{ 2 } \right) ^{ 5 } }{ \left( -\frac { 1 }{ 2 } \right) ^{ 4 } } \div \frac { \left( -\frac { 1 }{ 8 } \right) }{ \left( -\frac { 1 }{ 4 } \right) } \)is_____
- (a)
2
- (b)
0
- (c)
1
- (d)
-1
\(\left\{ \left( \frac { 1 }{ 3 } \right) ^{ -3 }-\left( \frac { 1 }{ 2 } \right) ^{ -3 } \right\} \div \left( \frac { 1 }{ 4 } \right) ^{ -3 }\)=?
- (a)
\(\frac { 19 }{ 24 } \)
- (b)
\(\frac { 64 }{ 19 } \)
- (c)
\(\frac { 27 }{ 16 } \)
- (d)
\(\frac { 16 }{ 27 } \)
The value of (- 8)\(\times\)(- 8)\(\times\)(- 8)\(\times\)(- 8)\(\times\)(- 8) + (- 8)\(\times\)(- 8)\(\times\)(- 8)\(\times\)(- 8)\(\times\)(- 8) is____
- (a)
-2(8)5
- (b)
-(2)16
- (c)
-(4)8
- (d)
All of these
\(\left\{ \left( \frac { 3 }{ 4 } \right) ^{ -1 }\left( \frac { 1 }{ 4 } \right) ^{ -1 } \right\} ^{ -1 }\)=?
- (a)
\(\frac { 3 }{ 8 } \)
- (b)
\(\frac { -3 }{ 8 } \)
- (c)
\(\frac { 8 }{ 3 } \)
- (d)
\(\frac { -8 }{ 3 } \)
If\(\left( \frac { 5 }{ 9 } \right) ^{ 4 }\times \left( \frac { 5 }{ 9 } \right) ^{ -10 }=\left( \frac { 5 }{ 9 } \right) ^{ -4 }\left( \frac { 5 }{ 9 } \right) ^{ 2a-1 }\)then the value of a is____
- (a)
1
- (b)
\(\frac { -5 }{ 2 } \)
- (c)
\(\frac { -5 }{ 4 } \)
- (d)
\(\frac { -1 }{ 2 } \)
If\(\left( \frac { 3 }{ 2 } \right) ^{ 2 }\times \left( \frac { 3 }{ 2 } \right) ^{ a+5 }=\left( \frac { 3 }{ 2 } \right) ^{ 8 }\)then a =______
- (a)
-1
- (b)
0
- (c)
1
- (d)
2
Which of the following statements is true?
Statement-1: If \(x={ \left( \frac { 2 }{ 3 } \right) }^{ 4 }\div { \left( \frac { 2 }{ 3 } \right) }^{ 2 },\) then value of x2 + 2x + 3 is 0.
Statement-2: If \({ \left( -\frac { 1 }{ 2 } \right) }^{ 4 }\times { (-2) }^{ 8 }={ (-2) }^{ 4x }\) then x = 1.
- (a)
Only Statement - 1
- (b)
Only Statement - 2
- (c)
Both Statement-1 and Statement-2
- (d)
Neither Statement-1 nor Statement-2
State 'T' for true and 'F' for false.
(P) If x and y are non-zero rational numbers and m is a positive integer,then
\({ x }^{ m }\times { y }^{ m }={ (xy) }^{ 2m }and\quad { x }^{ m }\div { y }^{ m }={ \left( \frac { x }{ y } \right) }^{ 1 }\)
(Q) Standard form of 38000000 is 3.8 \(\times\) 107
(R) The base and power in (-16 \(\times\) 2)4 is -32 and 4 respectively.
(S) 62 is greater than 26 .
- (a)
P Q R S T F F T - (b)
P Q R S F T T F - (c)
P Q R S F T F T - (d)
P Q R S T F T F
The value of\(\left( \frac { 23 }{ 25 } \right) ^{ 0 }\times \left( \frac { -1 }{ 2 } \right) ^{ 5 }\times { 2 }^{ 3 }\times \left( \frac { 3 }{ 4 } \right) ^{ 2 }\)is______
- (a)
\(-\frac { 9 }{ 64 } \)
- (b)
\(\frac { 9 }{ 64 } \)
- (c)
\(\frac { 64 }{ 9 } \)
- (d)
\(-\frac { 64 }{ 9 } \)
There are three places A, B, C in a straight line as shown below. If distance between place A and B is (2.4\(\times\)106) m and distance between place Band G is (5.2\(\times\)105) m, then find the distance between place A and G in standard form.
- (a)
(292\(\times\)106) km
- (b)
(2.92\(\times\)106) km
- (c)
(292\(\times\)105) km
- (d)
(292\(\times\)104) km
Compare the following and put the correct sign.
I. (32)3 \(\boxed{}\) \({ 3 }^{ 2^{ 3 } }\)
II. \((8^{ 4 })^{ \frac { 1 }{ 2 } }\) \(\boxed{}\) 24
III. \((8^{ 1/3 })^{ 9 }\) \(\boxed{}\) \((81^{ 1/4 })^{ 2 }\)
- (a)
I II III > < = - (b)
I II III < = > - (c)
I II III = < > - (d)
I II III < > >