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SubjectsMathematics
घातांक
In Class 9 Mathematics, the topic Exponents builds on Number Systems by showing how repeated multiplication is represented compactly using powers. Students learn to identify the base and exponent, apply the laws of exponents while multiplying and dividing powers, and work with zero and negative integral exponents. They practise simplifying numerical and algebraic expressions, compare powers, and use exponent notation accurately to express very large or very small numbers.
Correct answer: D. 10648
Explanation: An exponent of 3 means multiplying 22 three times: \(22^3=22\times22\times22\). First, \(22\times22=484\), and then \(484\times22=10648\). Therefore, 10648 is correct. A value such as 11648 can result from an error in multiplication. Exam tip: For a cube, find the square first and then multiply once more by the number.
Correct answer: A. 1681
Explanation: The square of 41 is \(41^2=41\times41\). Since \(40\times41=1640\) and \(1\times41=41\), the total is \(1640+41=1681\). Therefore, 1681 is correct. A value such as 1661 can result from a small addition or multiplication error. Exam tip: use \((a+1)^2=a^2+2a+1\), so \(41^2=(40+1)^2=1600+80+1=1681\).
Correct answer: B. 12167
Explanation: An exponent of 3 means multiplying 23 by itself three times: \(23^3=23\times23\times23\). First, \(23\times23=529\), and then \(529\times23=12167\). Therefore, 12167 is correct. The other options do not match this product. Exam tip: To find a cube, first square the number and then multiply by the same number.
Correct answer: C. 1764
Explanation: Here, 42² means multiplying 42 by itself: \(42 \times 42 = 42 \times (40+2) = 1680+84 = 1764\). Therefore, the correct answer is 1764. A value such as 1754 can result from an addition error during multiplication. Exam tip: To check a square, split the number using \((a+b)^2\) or the distributive property.
Correct answer: D. 13824
Explanation: An exponent of 3 means multiplying 24 three times: \(24^3=24\times24\times24\). First, \(24\times24=576\), and then \(576\times24=13824\). Therefore, the correct answer is 13824. The option 13834 results from an error in the final multiplication. Exam tip: to find a cube, first square the number and then multiply by the number once more.
Correct answer: A. 1849
Explanation: The square of a number is obtained by multiplying it by itself: \(43^2 = 43 \times 43 = 1849\). Therefore, 1849 is correct. A value such as 1839 may result from a small multiplication error, but it is not the square of 43. Exam tip: You can quickly verify it using \((40+3)^2 = 40^2 + 2\times40\times3 + 3^2\).
Correct answer: B. 15625
Explanation: An exponent of 3 means that 25 is multiplied by itself three times: \(25^3=25\times25\times25\). First, \(25\times25=625\), and then \(625\times25=15625\). Therefore, 15625 is correct. A value such as 14625 can result from an arithmetic error during multiplication. Exam tip: to find a cube, first find the square and then multiply it by the same number.
Correct answer: B. 1936
Explanation: \(44^2=(40+4)^2=40^2+2\cdot40\cdot4+4^2=1600+320+16=1936\). Hence the correct value is 1936. The nearest distractors 1926 and 1946 are off by 10, while 1956 is off by 20, so they are incorrect. Exam tip: use the \((a+b)^2\) expansion for quick mental squaring of two-digit numbers or memorize squares up to 50.
Correct answer: D. 17576
Explanation: An exponent of 3 means multiplying 26 by itself three times: \(26^3=26\times26\times26\). First, \(26\times26=676\), and then \(676\times26=17576\). Therefore, the correct answer is 17576. A value such as 16576 can result from an arithmetic error in multiplication. Exam tip: to find a cube, first find the square and then multiply it by the original number.
Correct answer: A. 2025
Explanation: Here, \(45^2\) means \(45 \times 45\). Therefore, \(45 \times 45 = 2025\), so 2025 is correct. 2015 is not the square of 45 and may result from an arithmetic error in multiplication. Exam tip: To find the square of a number, multiply it by itself.
Correct answer: B. 19683
Explanation: The exponent 3 means that 27 is multiplied by itself three times: \(27^3=27\times27\times27\). First, \(27\times27=729\), and then \(729\times27=19683\). Therefore, 19683 is correct. A value such as 18683 can result from an arithmetic error during multiplication. In exams, write a power as repeated multiplication to check the calculation.
Correct answer: C. 2116
Explanation: 46^2 = 46×46. Break the multiplication: 40×46 = 1840 and 6×46 = 276, so 1840+276 = 2116. Options A and B differ by ±10 (2106 and 2126) and represent common small arithmetic mistakes. Exam tip: use distributive splitting (e.g., 46=(40+6)) to compute squares mentally and avoid errors.
Correct answer: D. 21952
Explanation: An exponent of 3 means multiplying 28 by itself three times: \(28^3=28\times28\times28\). First, \(28\times28=784\), and then \(784\times28=21952\). Therefore, the correct answer is 21952. A value such as 20952 can result from an arithmetic error in multiplication. Exam tip: to find a cube, first find the square of the number and multiply it by the same number.
Correct answer: A. 2209
Explanation: \(47^2\) means \(47 \times 47\). Since \(47 \times 47 = 2209\), the correct answer is 2209. Although 2199 is close, it is not the square of 47. Exam tip: use \((50-3)^2 = 2500-300+9 = 2209\) to calculate the square quickly.
Correct answer: B. 24389
Explanation: An exponent of 3 means multiplying 29 by itself three times: \(29^3=29\times29\times29\). First, \(29\times29=841\), and then \(841\times29=24389\). Therefore, 24389 is correct. A value such as 23389 can result from an arithmetic error in multiplication. Exam tip: to find a cube, first square the number and then multiply by the number once more.
Correct answer: C. 216
Explanation: For multiplication with the same base add the exponents. Thus \(6^1\times6^2=6^{1+2}=6^3=216\). Option A (36) is incorrect — it corresponds to the wrong operation of multiplying exponents: \(6^{1\times2}=6^2=36\). Exam tip: add exponents for multiplication of same base; subtract for division.
Correct answer: C. 27000
Explanation: We need to find the cube of 30: \(30^3=30\times30\times30=900\times30=27000\). Therefore, 27000 is correct. The value 2700 has one zero too few. Exam tip: Write \(30=3\times10\), so \(30^3=3^3\times10^3=27\times1000\).
Correct answer: A. 2304
Explanation: Here, \(48^2\) means \(48 \times 48\). Since \(48 \times 48 = 2304\), the correct answer is 2304. A value such as 2204 is not the product of 48 and 48. Exam tip: To find the square of a number, multiply it by itself.
Correct answer: B. 29791
Explanation: An exponent of 3 means multiplying 31 by itself three times: \(31^3=31\times31\times31\). First, \(31\times31=961\), and then \(961\times31=29791\). Therefore, 29791 is correct. A value such as 30791 can result from a small multiplication error. In exams, find the square first and then multiply by the same number.
Correct answer: C. 100000
Explanation: An exponent shows how many times a number is multiplied by itself. Thus, \(10^5=10\times10\times10\times10\times10=100000\), so 100000 is correct. The close distractor 10000 equals \(10^4\), not \(10^5\). Exam tip: \(10^n\) has 1 followed by \(n\) zeros.
Correct answer: D. 2401
Explanation: Here, \(49^2\) means \(49\times49\). Using \((50-1)^2=50^2-2\times50\times1+1^2=2500-100+1=2401\), the correct answer is 2401. Although 2501 is close to \(50^2\), the square of 49 is 99 less than 2500. Exam tip: use \((a-b)^2=a^2-2ab+b^2\) to calculate squares near a convenient number such as 50.
Correct answer: A. 32768
Explanation: An exponent of 3 means multiplying 32 by itself three times: \(32^3=32\times32\times32=1024\times32=32768\). Therefore, 32768 is correct. Note that 1024 is the value of \(32^2\), not \(32^3\). Exam tip: In \(a^n\), multiply the base \(a\) by itself \(n\) times.
Correct answer: B. 2601
Explanation: To find the square of a number, multiply it by itself. Thus, \(51^2=51\times51=2601\), so 2601 is correct. A value such as 2501 does not result from multiplying 51 by 51. Exam tip: You can quickly verify it using \((50+1)^2=50^2+2\times50\times1+1^2\).
Correct answer: C. 35937
Explanation: An exponent of 3 means that 33 is multiplied by itself three times: \(33^3=33\times33\times33\). First, \(33\times33=1089\), and then \(1089\times33=35937\). Therefore, 35937 is the correct answer. The other options do not match this product. Exam tip: To find a cube, first square the number and then multiply by the same number.
Correct answer: D. 2704
Explanation: We need to find the square of 52: \(52^2=52\times52\). Thus, \(52\times52=52\times(50+2)=2600+104=2704\), so option D is correct. Option A, 2604, can result from a common addition error during multiplication. Exam tip: check a square using \((a+b)^2\) or the distributive property.
