Exponents

Correct answer: D. 1600

Explanation: An exponent of 2 means the square of the number. Therefore, \(40^2 = 40 \times 40 = 1600\). The value 400 is only \(40 \times 10\), so it is not correct. Exam tip: when squaring a number, multiply it by itself.

Correct answer: A. 484

Explanation: Here, \(22^2\) means \(22 \times 22\). Thus, \(22 \times 22 = 22 \times (20+2) = 440+44 = 484\), so 484 is correct. 444 may result from an error while multiplying 22 by 22. Exam tip: Rewrite \(n^2\) as \(n \times n\) to check the calculation.

Correct answer: B. 512

Explanation: An exponent of 3 means that 8 is multiplied by itself three times: \(8^3=8\times8\times8=64\times8=512\). Therefore, 512 is correct. The close distractor 64 is the value of \(8^2\), not \(8^3\). Exam tip: in \(a^n\), n tells how many times a is used as a factor.

Correct answer: A. 576

Explanation: The exponent 2 means that 24 is multiplied by itself: \(24^2 = 24 \times 24 = 576\). Therefore, 576 is the correct answer. A value such as 496 can result from incorrect multiplication. Exam tip: to find a square, multiply the number by itself.

Correct answer: C. 2500

Explanation: An exponent of 2 means multiplying the number by itself. Thus, \(50^2=50\times50=2500\). The value 500 is only \(50\times10\), not the square of 50. Exam tip: Write both factors when finding a square to avoid place-value errors.

Correct answer: A. 256

Explanation: \(2^8\) means multiplying 2 by itself eight times: \(2\times2\times2\times2\times2\times2\times2\times2=256\). Therefore, 256 is correct. Note that 128 is the value of \(2^7\), not \(2^8\). Exam tip: Remember consecutive powers of 2: \(2^6=64\), \(2^7=128\), and \(2^8=256\).

Correct answer: B. 625

Explanation: Here, \(25^2\) means the square of 25, that is, \(25 \times 25\). Therefore, \(25 \times 25 = 625\), so 625 is the correct answer. The numbers 525, 725, and 425 are not obtained by multiplying 25 by itself. Exam tip: To find a square, multiply the number by itself.

Correct answer: C. 243

Explanation: An exponent of 5 means that 3 is multiplied by itself five times: \(3^5=3\times3\times3\times3\times3=243\). Therefore, 243 is correct. Note that 81 is \(3^4\), while 729 is \(3^6\). Exam tip: if you know \(3^4=81\), multiply it by 3 to get \(3^5=243\).

Correct answer: D. 3600

Explanation: Here, 60^2 means 60 multiplied by itself: 60 × 60 = 3600. Therefore, 3600 is the correct answer. The value 600 is obtained by multiplying 60 by 10, not by squaring it. Exam tip: when a number ends in one zero, its square ends in two zeros.

Correct answer: A. 1024

Explanation: Here, 4 is multiplied by itself five times: \(4^5=4\times4\times4\times4\times4=1024\). Therefore, 1024 is the correct option. The value 256 is \(4^4\), so it is a close but incorrect distractor. Exam tip: In \(a^n\), the base \(a\) is multiplied by itself \(n\) times.

Correct answer: B. 529

Explanation: To find the square of 23, multiply 23 by itself: \(23^2 = 23 \times 23 = 529\). Therefore, 529 is the correct answer. Values such as 523 and 539 are not the correct products of 23 multiplied by 23. Exam tip: To square a number, multiply the number by itself.

Correct answer: C. 625

Explanation: An exponent of 4 means that 5 is multiplied by itself four times: \(5^4 = 5 \times 5 \times 5 \times 5 = 625\). Therefore, 625 is the correct answer. 3125 is the value of \(5^5\), so it is a close but incorrect option. Exam tip: Remember \(5^2=25\); then use \(5^4=(5^2)^2=25^2=625\).

Correct answer: D. 4900

Explanation: Here, \(70^2\) means \(70 \times 70\). Since \(7 \times 7 = 49\), and each factor 70 has one zero, the product has two zeros: \(70 \times 70 = 4900\). Therefore, 4900 is correct. The value 700 is not the square of 70. Exam tip: To find a square, multiply the number by itself.

Correct answer: A. 1

Explanation: For every non-zero number, the value of the zero exponent is 1. Therefore, \(3^0=1\). Do not choose 0 merely because the exponent is zero; a zero exponent does not make the base 3 equal to zero. Exam tip: remember that \(a^0=1\) only when \(a\ne0\).

Correct answer: B. 676

Explanation: Here, \(26^2\) means \(26 \times 26\). Since \(26 \times 26 = 676\), the correct answer is 676. Values such as 656 or 696 can result from an error while adding the tens and ones products. Exam tip: to find the square of a number, multiply the number by itself.

Correct answer: C. 64

Explanation: When powers with the same base are multiplied, their exponents are added: \(2^2\times2^4=2^{2+4}=2^6=64\). Therefore, 64 is correct. 16 is only the value of \(2^4\), so it misses multiplication by \(2^2\). Exam tip: For multiplication of like bases, add the exponents and retain the base.

Correct answer: D. 6400

Explanation: We need to find the square of 80: \(80^2 = 80 \times 80 = 6400\). Therefore, 6400 is correct. The value 640 is only \(8^2\) with one zero added incorrectly; multiplying two factors of 80 gives two zeros in the product. Exam tip: for squares of numbers such as 80, square 8 first and then append two zeros.

Correct answer: A. 729

Explanation: Here, \(27^2\) means \(27\times 27\). Since \(27\times 27=729\), the correct answer is 729. The option 7290 has an extra zero, so it is incorrect. Exam tip: To find the square of a number, multiply the number by itself.

Correct answer: B. 1296

Explanation: Here, 6 is multiplied by itself four times: 6 × 6 × 6 × 6 = 36 × 36 = 1296. Therefore, the correct answer is 1296. The value 216 is a close distractor because it equals 6^3, not 6^4. Exam tip: a^n means multiplying a by itself n times.

Correct answer: C. 784

Explanation: An exponent of 2 means multiplying the number by itself. Thus, 28^2 = 28 × 28 = 784, so 784 is correct. Values such as 774 or 794 can result from small multiplication errors. Exam tip: While finding a square, check the products of the ones and tens places separately.

Correct answer: D. 8100

Explanation: We need to find the square of 90: \(90^2 = 90 \times 90 = (9 \times 10)^2 = 81 \times 100 = 8100\). Therefore, the correct answer is 8100. The value 900 is not the square of 90; it equals \(90 \times 10\). Exam tip: when a number ends in one zero, its square ends in two zeros.

Correct answer: A. 841

Explanation: Here, \(29^2\) means \(29 \times 29\). Since \(29 \times 29 = 841\), the correct answer is 841. The numbers 831, 851, and 821 are not the square of 29. Exam tip: calculate quickly using \(29^2=(30-1)^2=900-60+1=841\).

Correct answer: B. 2401

Explanation: \(7^4\) means multiplying 7 by itself four times: \(7\times7\times7\times7=49\times49=2401\). Therefore, 2401 is correct. \(343\) is the value of \(7^3\), so it is a close but incorrect option. Exam tip: the exponent tells how many times the base is multiplied by itself.

Correct answer: C. 125

Explanation: When powers with the same base are multiplied, their exponents are added: \(5^1\times 5^2=5^{1+2}=5^3=125\). Therefore, the correct answer is 125. The value 25 is only \(5^2\), so it is not correct here. Exam tip: add exponents when multiplying like bases and subtract them when dividing.

Correct answer: D. 10000

Explanation: An exponent of 2 means multiplying 100 by itself: \(100^2=100\times100=10000\). Therefore, 10000 is the correct option. The values 1000, 100, and 100000 are not equal to this product. Exam tip: Since \(10^2=100\), \(100^2=(10^2)^2=10^4=10000\) is a quick method.