Exponents

Correct answer: A. A={11,13,17,19,23,29}

Explanation: The governing concept is converting a set-builder description into roster form. The strict inequalities require prime numbers greater than 10 and less than 30. Testing the primes in that interval gives 11, 13, 17, 19, 23, and 29. Number 21 is composite, 31 is outside the interval, and 10 and 30 are excluded by strict inequalities. Therefore option A is correct.

Correct answer: A. 8

Explanation: Here, 2 is the base and 3 is the exponent. Therefore, \(2^3=2\times2\times2=8\), so 8 is correct. A common mistake is choosing 6 by calculating \(2\times3\), but an exponent does not mean multiplication by the exponent. Exam tip: In \(a^n\), multiply the base \(a\) by itself \(n\) times.

Correct answer: C. 25

Explanation: The exponent 2 means that 5 is multiplied by itself: \(5^2=5\times5=25\). Option 10 is the product of 5 and 2, but it is not the value of \(5^2\). Exam tip: \(a^2\) always means \(a\times a\).

Correct answer: B. 100

Explanation: An exponent of 2 means that 10 is multiplied by itself twice: \(10^2=10\times10=100\). Therefore, 100 is correct. The number 20 is twice 10, but it is not the value of \(10^2\). Exam tip: in \(a^n\), n tells how many times the base a is multiplied by itself.

Correct answer: C. 9

Explanation: The exponent 2 means that 3 is multiplied by itself twice: \(3^2=3\times3=9\). Therefore, 9 is correct. The value 6 comes from multiplying 3 by 2, but an exponent represents repeated multiplication. Exam tip: Check \(a^2\) by writing it as \(a\times a\).

Correct answer: D. 16

Explanation: An exponent of 2 means multiplying 4 by itself: \(4^2=4\times4=16\). Therefore, 16 is correct. The number 8 is twice 4, not its square. Exam tip: Check \(a^2\) by writing it as \(a\times a\).

Correct answer: A. 7

Explanation: By the exponent rule, any number raised to the power 1 remains the same number. Therefore, \(7^1=7\). Option 1 is the value of \(7^0\), while 49 is the value of \(7^2\). Exam tip: Remember \(a^1=a\) and \(a^0=1\), where \(a\ne0\), as different rules.

Correct answer: B. 1

Explanation: For any positive integer exponent, multiplying 1 by itself any number of times still gives 1. Therefore, \(1^8=1\). The number 8 is the exponent, not the value. Exam tip: \(1^n=1\) for every positive integer \(n\).

Correct answer: C. 16

Explanation: An exponent of 4 means that 2 is multiplied by itself four times: \(2^4=2\times2\times2\times2=16\). Therefore, 16 is the correct answer. The value 8 is \(2^3\), so it is a close but incorrect option. Exam tip: in \(a^n\), multiply the base \(a\) by itself \(n\) times.

Correct answer: D. 81

Explanation: An exponent of 2 means that 9 is multiplied by itself: \(9^2=9\times9=81\). Therefore, 81 is the correct answer. 90 is not the square of 9. Exam tip: Check \(a^2\) by writing it as \(a\times a\).

Correct answer: A. 32

Explanation: When powers with the same base are multiplied, their exponents are added: \(2^2\times2^3=2^{2+3}=2^5=32\). Therefore, 32 is correct. Getting 16 results from incorrectly multiplying the exponents. Exam tip: add exponents when multiplying like bases, and subtract them when dividing.

Correct answer: B. 27

Explanation: The exponent 3 means that the base 3 is multiplied by itself three times: \(3^3=3\times3\times3=27\). Therefore, 27 is correct. 9 is the value of \(3^2\), while 81 is the value of \(3^4\). Exam tip: in \(a^n\), n tells how many times a is used as a factor.

Correct answer: C. 36

Explanation: An exponent of 2 means that 6 is multiplied by itself: \(6^2=6\times6=36\). Therefore, 36 is correct. The value 12 is twice 6, not its square. Exam tip: Rewrite \(a^2\) as \(a\times a\) before calculating.

Correct answer: D. 64

Explanation: An exponent of 2 means that 8 is multiplied by itself: \(8^2=8\times8=64\). Therefore, the correct answer is 64. Note that 16 is \(4^2\), not the square of 8. Exam tip: Rewrite \(a^2\) as \(a\times a\) before calculating.

Correct answer: A. 1000

Explanation: An exponent of 3 means that 10 is multiplied by itself three times: \(10^3=10\times10\times10=1000\). Therefore, 1000 is correct. The value 100 is a close distractor because it equals \(10^2\), not \(10^3\). Exam tip: In \(a^n\), n tells how many times a is used as a factor.

Correct answer: B. 64

Explanation: The exponent 3 means that 4 is multiplied by itself three times: \(4^3=4\times4\times4=64\). Therefore, 64 is correct. The value 16 is \(4^2\), 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: C. 1

Explanation: Any non-zero number raised to the power 0 equals 1. Therefore, \(5^0=1\). Choosing 0 is a common error from applying exponent rules incorrectly; here the base, 5, is non-zero. Exam tip: remember that \(a^0=1\) only when \(a\ne0\).

Correct answer: D. 49

Explanation: An exponent of 2 means multiplying 7 by itself: \(7^2 = 7 \times 7 = 49\). Therefore, 49 is the correct answer. The value 14 comes from \(7+7\), not from squaring 7. Exam tip: Rewrite \(a^2\) as \(a \times a\) before calculating.

Correct answer: A. 32

Explanation: An exponent of 5 means that 2 is multiplied by itself five times: \(2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32\). Therefore, 32 is the correct option. 16 is \(2^4\), while 64 is \(2^6\). Exam tip: each successive power of 2 is double the preceding power.

Correct answer: B. 27

Explanation: When powers with the same base are multiplied, their exponents are added: \(3^2\times 3^1=3^{2+1}=3^3=27\). Therefore, 27 is correct. \(9\) is only the value of \(3^2\), whereas \(81\) equals \(3^4\). Exam tip: use \(a^m\times a^n=a^{m+n}\) only when the bases are the same.

Correct answer: C. 121

Explanation: An exponent of 2 means that 11 is multiplied by itself: \(11^2 = 11 \times 11 = 121\). Therefore, 121 is the correct answer. 111 is not the square of 11. Exam tip: To find a square, multiply the number by itself.

Correct answer: D. 144

Explanation: Here, \(12^2\) means the square of 12, that is, \(12 \times 12\). Since \(12 \times 12 = 144\), the correct answer is 144. A number such as 132 is not obtained by squaring 12. Exam tip: Read \(n^2\) as \(n \times n\) before multiplying.

Correct answer: A. 1

Explanation: For any non-zero number, the zero-exponent rule is \(a^0=1\). Therefore, \(1^0=1\). Option 0 is not correct; \(0^0\) is generally treated as undefined/indeterminate, but the base here is 1. Exam tip: Do not write 0 merely because the exponent is 0.

Correct answer: B. 64

Explanation: Here, 2 is multiplied by itself 6 times: \(2^6=2\times2\times2\times2\times2\times2=64\). Therefore, 64 is correct. The nearby distractor 32 equals \(2^5\), not \(2^6\). Exam tip: an exponent \(n\) tells how many times the base is used as a factor.

Correct answer: C. 169

Explanation: An exponent of 2 means that 13 is multiplied by itself: \(13^2 = 13 \times 13 = 169\). Therefore, 169 is the correct option. Note that 143 equals \(13 \times 11\), not the square of 13. Exam tip: to find a square, multiply the number by itself.