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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: B. 225
Explanation: An exponent of 2 means multiplying 15 by itself: \(15^2 = 15 \times 15 = 225\). Therefore, 225 is the correct answer. 215 is not the square of 15. Exam tip: To find the square of a number, multiply the number by itself.
Correct answer: A. 8
Explanation: When powers with the same base are multiplied, their exponents are added: \(2^1\times2^2=2^{1+2}=2^3=8\). Therefore, the correct answer is 8. The value 4 is only \(2^2\), so it is not correct. Exam tip: use \(a^m\times a^n=a^{m+n}\) only when the bases are the same.
Correct answer: B. 196
Explanation: An exponent of 2 means multiplying 14 by itself: \(14^2 = 14 \times 14 = 196\). Therefore, 196 is the correct option. 144 is a close distractor because it equals \(12^2\), not \(14^2\). Exam tip: To find a square, multiply the number by itself.
Correct answer: C. 81
Explanation: The exponent 4 means that 3 is multiplied by itself four times: \(3^4=3\times3\times3\times3=81\). Therefore, 81 is the correct answer. The value 27 is \(3^3\), so it is a close but incorrect option. Exam tip: In \(a^n\), n tells how many times a is used as a factor.
Correct answer: D. 256
Explanation: In an exponent, 16^2 means multiplying 16 by itself: 16 \times 16 = 256. Therefore, the correct answer is 256. The value 196 is 14^2, not 16^2. Exam tip: To find the square of a number, multiply the number by itself.
Correct answer: A. 9
Explanation: Any number raised to the power 1 equals the number itself: \(a^1=a\). Therefore, \(9^1=9\). The value 81 is \(9^2\), so it is not correct here. Exam tip: when the exponent is 1, write the base directly.
Correct answer: A. 324
Explanation: The square of a number is found by multiplying the number by itself. Thus, \(18^2 = 18 \times 18 = 324\), so 324 is correct. 288 is not the square of 18. Exam tip: You can also check \(18^2\) using \((20-2)^2\).
Correct answer: B. 125
Explanation: In \(5^3\), 5 is the base and 3 is the exponent. It means \(5\times5\times5=125\), so 125 is the correct option. The value 25 is \(5^2\), not \(5^3\). Exam tip: in \(a^n\), multiply the base \(a\) by itself \(n\) times.
Correct answer: C. 128
Explanation: \(2^7\) means multiplying 2 by itself seven times: \(2\times2\times2\times2\times2\times2\times2=128\). Therefore, the correct answer is 128. The value 64 is \(2^6\), so it is a close but incorrect option. Exam tip: each successive power of 2 is double the preceding power.
Correct answer: D. 400
Explanation: To find the square of a number, multiply it by itself. Thus, \(20^2=20\times20=400\), so 400 is correct. The value 200 is obtained by multiplying 20 by 10, not by squaring it. Exam tip: \(a^2\) always means \(a\times a\).
Correct answer: A. 216
Explanation: An exponent of 3 means that 6 is multiplied by itself three times: \(6^3=6\times6\times6=216\). Therefore, the correct answer is 216. The value 36 is \(6^2\), not \(6^3\). Exam tip: in \(a^n\), multiply the base \(a\) by itself \(n\) times.
Correct answer: B. 16
Explanation: When powers with the same base are multiplied, their exponents are added: \(2^3\times2^1=2^{3+1}=2^4=16\). Therefore, the correct answer is 16. The value 8 is only \(2^3\); it does not include multiplication by \(2^1\). Exam tip: use \(a^m\times a^n=a^{m+n}\) only when the bases are the same.
Correct answer: C. 25
Explanation: For any number, an exponent of 1 leaves the base unchanged: \(a^1=a\). Therefore, \(25^1=25\). Option 1 is the value of \(25^0\), while 625 equals \(25^2\). Exam tip: when the exponent is 1, write the base as it is.
Correct answer: D. 0
Explanation: The exponent 5 is a positive integer, so \(0^5=0\times0\times0\times0\times0=0\). Option 1 is associated with the rule \(a^0=1\), but that rule does not apply to \(0^5\); \(0^0\) is a separate case. Exam tip: Any positive power of zero is zero.
Correct answer: A. 289
Explanation: An exponent of 2 means the square of the number. Thus, \(17^2=17\times17=289\), so 289 is correct. The values 279, 299, and 269 are not obtained by multiplying 17 by 17. Exam tip: Check a square using direct multiplication or \((10+7)^2\).
Correct answer: B. 343
Explanation: An exponent of 3 means that 7 is multiplied by itself three times: \(7^3 = 7 \times 7 \times 7 = 343\). Therefore, 343 is correct. The value 392 comes from \(7 \times 7 \times 8\), so it is not \(7^3\). Exam tip: in \(a^3\), multiply the base \(a\) exactly three times.
Correct answer: C. 100
Explanation: Any number raised to the power 1 remains the same: \(a^1=a\). Therefore, \(100^1=100\). The value 1000 would result from multiplying 100 by 10, not from raising it to the power 1. Exam tip: when the exponent is 1, write the base directly.
Correct answer: D. 900
Explanation: An exponent of 2 means multiplying the number by itself. Thus, \(30^2 = 30 \times 30 = 900\). The option 300 may result from an incorrect place-value calculation instead of squaring 30. Exam tip: for a square, always multiply the number by itself.
Correct answer: A. 256
Explanation: An exponent of 4 means that 4 is multiplied by itself four times: \(4^4=4\times4\times4\times4=16\times16=256\). Therefore, 256 is correct. The value 64 is \(4^3\), so it is a close but incorrect option. Exam tip: in \(a^n\), n tells how many times a is used as a factor.
Correct answer: B. 8
Explanation: Any number raised to the power 1 remains unchanged: \(a^1=a\). Therefore, \(8^1=8\). The value \(64\) is \(8^2\), not \(8^1\). Exam tip: When the exponent is 1, the answer is the base itself.
Correct answer: C. 361
Explanation: Here, \(19^2\) means \(19 \times 19\). Since \(19 \times 19 = 361\), the correct answer is 361. The number 351 is not the square of 19. Exam tip: To find the square of a number, multiply the number by itself.
Correct answer: D. 1
Explanation: For every non-zero number \(a\), \(a^0=1\). Since 2 is non-zero, \(2^0=1\). Option 0 is incorrect because an exponent of zero does not mean multiplying the number by zero. Exam tip: use \(a^0=1\) only when \(a\ne0\).
Correct answer: A. 81
Explanation: When powers with the same base are multiplied, their exponents are added: \(3^2\times3^2=3^{2+2}=3^4=81\). Therefore, the correct answer is 81. The value 27 is \(3^3\), so it is not correct. Exam tip: Use \(a^m\times a^n=a^{m+n}\) only when the bases are the same.
Correct answer: B. 441
Explanation: Here, \(21^2\) means \(21\times 21\). Therefore, \(21\times 21=441\), so 441 is correct. 421 is not the square of 21. Exam tip: To find a square, multiply the number by itself.
Correct answer: C. 729
Explanation: In an exponent, 9^3 means multiplying 9 by itself three times: 9\times 9\times 9 = 81\times 9 = 729. Therefore, 729 is the correct answer. 819 may result from an incorrect multiplication rather than cubing 9. Exam tip: to find a^3, first calculate a^2 and then multiply it by a once more.
