Olympiad 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 27 x 53?
- (a)
7500
- (b)
16000
- (c)
11200
- (d)
14000
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
(-11)2 x (-11)4 =(-11 )x. What is the value of x?
- (a)
2
- (b)
4
- (c)
6
- (d)
-2
Evaluate \(\left( \frac { 5 }{ 6 } \right) ^{ 5 }\).
- (a)
\(\left( \frac { 6 }{ 5 } \right) ^{ 5 }\).
- (b)
(56)5
- (c)
\(\frac { { 5 }^{ 5 } }{ 6^{ 5 } } \).
- (d)
(55)6
Express (-2)3 ÷ m3 in the form \(\left( \frac { a }{ b } \right) ^{ m }\) .
- (a)
\(\frac { -2^{ 3 } }{ m^{ 3 } } \).
- (b)
\(\left( -\frac { 2 }{ m } \right) ^{ 3 }\).
- (c)
\(\frac { (-2) }{ { m }^{ 3 } } \).
- (d)
\(-\left( \frac { 2 }{ m } \right) \left( \frac { -2 }{ m } \right) \).
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)
\(\frac { { 2 }^{ 6 }\times { 3 }^{ 2 } }{ { 5 }^{ 2 } } \).
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)
\(\frac { 1 }{ 5 } \left[ \frac { { n }^{ 2 } }{ m6^{ 10 } } \right] ^{ \frac { 2 }{ 3 } }\).
Solve 94x ÷ 32x=2187
- (a)
x=\(\frac { 6 }{ 7 } \).
- (b)
x=\(\frac { -7 }{ 6 } \)
- (c)
x=\(\frac { 7 }{ 6 } \) .
- (d)
x=\(\frac { -6 }{ 7 } \) .
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)
Express 62 x 7-4 x (8-2)2 x 63 x 72 x 84 in the simplest exponential form.
- (a)
6572
- (b)
\(\frac { { 6 }^{ 5 } }{ { 7 }^{ 2 } } \).
- (c)
6-572
- (d)
6-57-2
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 mass of the Earth is 5,976,000,000, 000,000,000,000,000 kg. How is the mass of Earth expressed in standard form
- (a)
5.976 x 1024kg
- (b)
5.976 x 1021kg
- (c)
5976 x 1021kg
- (d)
59.76x1023kg
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
Which is greater 23 or 52?
- (a)
Both are equal
- (b)
23
- (c)
52
- (d)
Cannot be determined.
Simplify \(\frac { { 64 }^{ 2x }\div { 16 }^{ x } }{ 128^{ x }\times { 4 }^{ 2x } } \).
- (a)
2-3x
- (b)
28x
- (c)
23x
- (d)
211x
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)
\(\frac { 16 }{ 27 } \)
If\(\left( \frac { 5 }{ 3 } \right) ^{ -5 }\times \left( \frac { 5 }{ 3 } \right) ^{ 11 }=\left( \frac { 5 }{ 3 } \right) ^{ 8+x }\),then x = ?
- (a)
\(\frac { -1 }{ 2 } \)
- (b)
-2
- (c)
2
- (d)
\(\frac { 1 }{ 2 } \)
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)
\(\frac { -1 }{ 2 } \)
Which of the following is equivalent to 7.7\(\times\)10-6?
- (a)
0.00000077
- (b)
0.0000077
- (c)
0.000077
- (d)
0.00077
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
Fill in the blanks.
(i) A number is said to be in the ___________ form, if it is expressed as the product of a number between 1 and 10 and the integral power of 10.
(ii) 20 \(\times\) 30 + 10 \(\times\) 3 = ________
(iii) ((22)2 \(\times\) 72) \(\div \) (83 \(\times\)7) = _______________
- (a)
(i) (ii) (iii) Standard 4 7\(\times\)2-5 - (b)
(i) (ii) (iii) Exponential 4 7\(\times\)2-4 - (c)
(i) (ii) (iii) Exponential 2 7\(\times\)25 - (d)
(i) (ii) (iii) Standard 2 7\(\times\)24
The value of ab-ba , if a = 3 and b = 7 is______
- (a)
1825
- (b)
1840
- (c)
1844
- (d)
1850
Mr Gupta asked two of his students to solve the expression\(\left( \frac { 9{ a }^{ 3 }{ b }^{ -8 } }{ 81{ a }^{ -5 }{ b }^{ 2 } } \right) ^{ -\frac { 1 }{ 2 } }\)and write the answer on blackboard. Aryan wrote the answer as 3 a-4b5 whereas Ayan wrote the answer as\(\frac { 3b^{ 5 } }{ { a }^{ 4 } } \)Who wrote the correct answer?
- (a)
Aryan
- (b)
Ayan
- (c)
Both of them
- (d)
None of these