Exponents

\(2^8\) 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 \(2^8=256\).

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.

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 \(3^5=243\).

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.

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.

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.

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 \(5^4=(5^2)^2=25^2=625\).

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.

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 \(a\ne0\).

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.

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.

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.

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.

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.

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.

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.

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 \(29^2=(30-1)^2=900-60+1=841\).

\(7^4\) 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.

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.

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.