Exponents

Here, 31^2 means the square of 31, that is, 31 × 31. Multiplying gives 31 × 31 = 961, so 961 is the correct option. Although close, 991 equals 31 × 32, not 31 × 31. Exam tip: To find the square of a number, multiply the number by itself.

Solution: \(9^2=81\), \(9^3=729\). Thus \(9^4=9^3\times9=729\times9=6561\). Alternatively, since \(9=(3^2)\), \(9^4=(3^2)^4=3^8=6561\). Explanation of distractors: 729 is \(9^3\), 59049 equals \(9^5\), and 5901 is an arithmetic error. Exam tip: compute successive powers or convert the base to prime factors (e.g. \(9=3^2\)) to find higher powers quickly.

An exponent of 2 means multiplying 32 by itself: \(32^2=32\times32=1024\). Therefore, 1024 is correct. 64 is the result of \(32\times2\), not \(32^2\). Exam tip: Do not treat an exponent as a number to multiply directly.

An exponent of 3 means multiplying 11 by itself three times: \(11^3=11\times 11\times 11=121\times 11=1331\). Therefore, the correct answer is 1331. While 121 is \(11^2\), 14641 is \(11^4\). Exam tip: multiply the base by itself as many times as indicated by the exponent.

Here, we need to find the square of 33: \(33^2=33\times33\). Therefore, \(33\times33=1089\), so 1089 is the correct option. The values 1079, 1099, and 1069 are not equal to the square of 33. Exam tip: You can quickly verify it using \(33^2=(30+3)^2=900+180+9=1089\).

An exponent of 3 means that 12 is multiplied by itself three times: \(12^3=12\times12\times12=144\times12=1728\). Therefore, 1728 is correct. Option 144 is the value of \(12^2\), not \(12^3\). Exam tip: In \(a^3\), the base \(a\) appears as three factors.

Here, 34^2 means the square of 34, i.e., 34 × 34. We get 34 × 34 = 34 × (30 + 4) = 1020 + 136 = 1156. Therefore, 1156 is correct. A choice such as 1146 can result from an error in multiplication or addition. Exam tip: Split a two-digit number into tens and ones while finding its square to reduce calculation errors.

An exponent of 3 means multiplying 13 by itself three times: \(13^3=13\times13\times13\). First, \(13\times13=169\), and then \(169\times13=2197\). Therefore, the correct answer is 2197. The value 169 is \(13^2\), so it is a close but incorrect option. Exam tip: Rewrite \(a^3\) as \(a\times a\times a\) before calculating.

Here, 35^2 means the square of 35, that is, 35 × 35. Therefore, 35 × 35 = 1225, so 1225 is the correct answer. An option such as 1215 can result from an arithmetic error during multiplication. Exam tip: To find the square of a number, multiply the number by itself.

An exponent of 3 means that 14 is multiplied by itself three times: \(14^3=14\times14\times14\). First, \(14\times14=196\), and then \(196\times14=2744\). Therefore, the correct answer is 2744. A number such as 2644 may result from an arithmetic error, but it is not the cube of 14. Exam tip: To find a cube, first find the square and then multiply it by the original number.

Here, 36² means multiplying 36 by itself: 36 × 36 = 1296. Therefore, the correct answer is 1296. The number 1269 is formed by reversing digits and is not the correct square. Exam tip: After squaring a number, check the digit order and place values in your final answer.

Here, \(15^3\) means \(15\times15\times15\). First, \(15\times15=225\), and then \(225\times15=3375\). Therefore, the correct answer is 3375. A value such as 3275 can result from an arithmetic error in multiplication. Exam tip: in \(a^3\), the base \(a\) is multiplied by itself three times.

The square of a number is obtained by multiplying it by itself. Thus, \(37^2=37\times37=1369\), so 1369 is correct. A value such as 1379 is not the product of \(37\times37\). Exam tip: you can quickly verify it using \((40-3)^2=40^2-2\times40\times3+3^2\).

An exponent of 3 means multiplying 16 by itself three times: \(16^3=16\times16\times16=256\times16=4096\). Therefore, 4096 is correct. A value such as 3096 can result from an incorrect multiplication. Exam tip: First find \(16^2=256\), then multiply 256 by 16.

The square of a number is obtained by multiplying the number by itself. Thus, \(38^2=38\times38=1444\). Therefore, 1444 is the correct option. A number such as 1454 may look close, but it is not obtained on multiplication. Exam tip: You can also verify it using \((40-2)^2\).

An exponent of 3 means multiplying 17 by itself three times: \(17^3=17\times17\times17\). First, \(17\times17=289\), and then \(289\times17=4913\). Therefore, the correct answer is 4913. A value such as 4893 can result from a small multiplication error. Exam tip: to find a cube, first calculate the square and then multiply by the original number.

The square of a number is obtained by multiplying the number by itself. Thus, \(39^2=39\times39=1521\). Therefore, 1521 is the correct option. A value such as 1531 may result from a small addition error, but the correct product is 1521. Exam tip: You can quickly verify it using \(39^2=(40-1)^2=1600-80+1\).

In exponent form, \(18^3\) means \(18\times18\times18\). First, \(18\times18=324\), and then \(324\times18=5832\). Therefore, the correct answer is \(5832\). Values such as 5732 or 5830 result from multiplication errors. Exam tip: To find a cube, first square the number and then multiply by the same number.

An exponent of 9 means multiplying 2 by itself nine times: \(2^9=2\times2\times2\times2\times2\times2\times2\times2\times2=512\). Therefore, 512 is correct. The close distractor 256 equals \(2^8\), not \(2^9\). Exam tip: Remember consecutive powers of 2; doubling \(2^8=256\) gives \(2^9=512\).

An exponent of 3 means multiplying 19 by itself three times: \(19^3=19\times19\times19\). First, \(19\times19=361\), and then \(361\times19=6859\). Therefore, 6859 is correct. A value such as 6759 can result from an arithmetic error in multiplication. Exam tip: to find a cube, first square the number and then multiply by the same number.

When powers with the same base are multiplied, their exponents are added: \(4^1\times4^2=4^{1+2}=4^3=64\). Therefore, 64 is the correct answer. Getting 32 does not apply the law of exponents correctly. Exam tip: use \(a^m\times a^n=a^{m+n}\) only when the bases are the same.

An exponent of 3 means multiplying 20 by itself three times: \(20^3 = 20 \times 20 \times 20 = 400 \times 20 = 8000\). Therefore, 8000 is the correct answer. The value 4000 would be \(20 \times 20 \times 10\), so it is not correct. Exam tip: To find a cube, multiply the number by itself three times.

Multiplying 1 by itself any number of times always gives 1. Therefore, \(1^{25}=1\). Here, 25 is the exponent, not the value of the expression. Exam tip: \(1^n=1\) for every positive integer \(n\).

An exponent of 3 means that 21 is multiplied by itself three times: \(21^3=21\times21\times21=441\times21=9261\). Therefore, option B is correct. A nearby value such as 9161 can result from an arithmetic error in multiplication. Exam tip: first find \(21^2=441\), then multiply it by 21.

An exponent of 4 means multiplying 10 by itself four times: \(10^4=10\times10\times10\times10=10000\). Therefore, 10000 is correct. The close distractor 1000 equals \(10^3\), not \(10^4\). Exam tip: \(10^n\) has 1 followed by \(n\) zeros.