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An exponent of a number indicates how many times a number is multiplied by itself. For example, 24 indicates that we have multiplied 2 four times. The enlarged form is 2 × 2 × 2 × 2. Exponent is sometimes known as a number’s power. It can be an integer, a fraction, a negative number, or decimals. In the above example, 2 is referred to as “base,” while 4 is referred to as the “exponent” or “power.” In general, it can be written as xn where x has been multiplied by itself n times. When a number from 0 to 9 is multiplied by a power of 10, it is considered to be expressed in scientific notation. When a number is larger than one, the power of ten is a positive exponent; when a number is less than one, the power of ten is negative.
Also read: Difference Between Power And Exponent: Definition and Explanation
1. am × an is equal to
(a) a(m + n)
(b) a(m – n)
(c) amn
(d) a(n – m)
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Answer: (a) a(m+n)
Explanation:
am + an = a × a × a × a × a (m times)
× a × a × a × a × (n time) = a (m + n) times
= a(m+n)
2. am ÷ an is equal to
(a) a(m − n)
(b) a(m+n)
(c) amn
(d) a(n – m)
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Answer: (a) a(m− n)
Explanation:
am ÷ an = a × a × a × a × a (m times)
/ a × a × a × a × (n times) = a (m − n) times
a(m − n)
3. (am)n is equal to
(a) am + n
(b) am − n
(c) amn
(d) an − m
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Answer: (c) amn
Explanation:
(am)n = a(m × n) asserts that multiplying a number, a, by itself m times, then multiplying that result by itself n times is the same as multiplying a by itself m × n times.
Let’s work out an example in which
a = 3
m = 4
n = 5
(am)n = a(m × n)
(34)5 = 3(4 × 5) = 320
= 3,486,784,401
4. If a ≠ 0, then the value of a0 is
(a) 0
(b) 1
(c) 2
(d) −1
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Answer: (b) 1
Explanation:
Any number, especially a non-zero integer, raised to the
power of 0 has the value 1. Therefore, a0 is 1.
5. Find the multiplicative inverse for the given
expression. The expression is 7−2
(a) 72
(b) 7
(c) 1/72
(d) 1/7
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Answer: (a) 72
Explanation:
The multiplicative inverse of any value is the one that yields a value equal to one when multiplied by the original value. Therefore, the multiplicative inverse of 7−2 is 72.
6. 22 x 23 x 24 can
be expressed as
(a) 224
(b) 2−5
(c) 29
(d) 2−9
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Answer: (c) 29
Explanation:
By laws of exponents,
am × an = am + n
22 × 23 × 24 = 22 + 3
+ 4 = 29
7. (−1)20 =
(a) −1
(b) 1
(c) 0
(d) 20
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Answer: (b) 1
Explanation:
(−1)20 is equivalent to 1 because raising a negative number to the power of an even integer results in a positive value. In this case, we multiply (−1) 20 times which results in the positive number, that is 1.
8. In 102, the exponent is
(a) 1
(b) 2
(c) 10
(d) 1.
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Answer: (b)
Explanation:
Consider an expression anb. Here, an is the base and b is the exponent, therefore in 102, 2 is the exponent.
9. The multiplicative inverse of 2/3 is
(a) 2/3
(b) 3/2
(c) 3
(d) 1
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Answer: (b) 3/2
Explanation: The
reciprocal of an integer is its multiplicative inverse.
3/2 is the multiplicative inverse of 2/3.
It is the multiplicative inverse because the result should
be 1 if you multiply both numbers (number and it’s reciprocal).
10. 3² × 3−4 × 35 is equal to
(a) 3
(b) 3²
(c) 3³
(d) 35
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Answer: (c) 33
By laws of exponents,
am × an = am + n
3² × 3−4 × 35 = 32 − 4 + 5
= 37 − 4
= 3³
11. 149600000000 is equal to
(a) 1.496 × 1011
(b) 1.496 × 1010
(c) 1.496 × 1012
(d) 1.496 × 108
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Answer: (a) 1.496 × 1011
Explanation:
The given number is 149600000000
This can be written as 1.496 × 100000000000
On moving the decimal point towards the left, it can be
written as 1.496 × 1011. 1011 is written since the
decimal point has been moved 11 places.
12. 0.00001275 is equal to
(a) 1.275 × 10−5
(b) 1.275 × 10−3
(c) 1.275 × 104
(d) 1.275 × 103
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Answer: (a) 1.275 × 10−5
Explanation:
The standard form of decimals is used to represent huge numbers into the smallest by multiplying the number by 10 to the power of the places it is separated from the decimal. Here, the decimal point is moved five numbers to the right; therefore, it indicates negative power, that is 10−5.
13. The value of 2−2 is
(a) 4
(b) ¼
(c) 2
(d) ½
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Answer: (b) ¼
Explanation:
We know that 2−2 = 0.25
Therefore, 2−2 = ¼
14. The multiplicative inverse of is
(a) 2−2
(b) 22
(c) 2
(d) 1
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Answer: (b) 22
Explanation:
The multiplicative inverse of any value is the one that yields a value equal to one when multiplied by the original value.
= 2−2
Therefore, the multiplicative inverse of 2−2 is 22.
15. 3−2 × 3−5 is equal to
(a) 3−7
(b) 3−3
(c) 3−10
(d) 37
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Answer: (a) 3−7
Explanation:
By laws of exponents,
am × an = am + n
3−2 × 3−5 = (1/32) × (1/35)
= (1/32+5)
= (1/37)
= 3−7
16. The value of (34)3 is
(a) 3
(b) 312
(c) 37
(d) None of the above
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Answer: (b) 312
Explanation:
By laws of exponents,
(am)n = amn
(34)3 = 34×3 = 312
17. 32 × 42 is equal to
(a) 121
(b) 49
(c) 144
(d) 156
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Answer: (c) 144
Explanation:
By law of exponents,
am × bm = (ab)m
32 × 42 = (3 × 4)2 = 122
= 144
18. 1000+200+50 is
equal to
(a) 125
(b) 25
(c) 1/125
(d) 3
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Answer: (d)
Explanation:
We know that anything to the power 0 is 1, that is a0 = 1
1000 + 200 + 50 = 1 + 1 + 1
= 3
19. If (–3)m + 1 × (–3)5 =
(–3)7, then the value of m is:
(a) 5
(b) 7
(c) 1
(d) 3
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Answer: (c) 1
Explanation:
By laws of exponents,
am × an = am + n
(−3)m + 1 × (−3)5=(−3)7
(−3)m + 1 + 5 = (−3)7
(−3)m + 6 = (−3)7
Powers on both sides have the same base, which is distinct
from 1 and −1. Hence their exponents must be equal. m = 7 − 6 = 1
m = 1.
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