Exponents

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.

An exponent of 3 means multiplying 22 three times: \(22^3=22\times22\times22\). First, \(22\times22=484\), and then \(484\times22=10648\). Therefore, 10648 is correct. A value such as 11648 can result from an error in multiplication. Exam tip: For a cube, find the square first and then multiply once more by the number.

The square of 41 is \(41^2=41\times41\). Since \(40\times41=1640\) and \(1\times41=41\), the total is \(1640+41=1681\). Therefore, 1681 is correct. A value such as 1661 can result from a small addition or multiplication error. Exam tip: use \((a+1)^2=a^2+2a+1\), so \(41^2=(40+1)^2=1600+80+1=1681\).

An exponent of 3 means multiplying 23 by itself three times: \(23^3=23\times23\times23\). First, \(23\times23=529\), and then \(529\times23=12167\). Therefore, 12167 is correct. The other options do not match this product. Exam tip: To find a cube, first square the number and then multiply by the same number.

Here, 42² means multiplying 42 by itself: \(42 \times 42 = 42 \times (40+2) = 1680+84 = 1764\). Therefore, the correct answer is 1764. A value such as 1754 can result from an addition error during multiplication. Exam tip: To check a square, split the number using \((a+b)^2\) or the distributive property.

An exponent of 3 means multiplying 24 three times: \(24^3=24\times24\times24\). First, \(24\times24=576\), and then \(576\times24=13824\). Therefore, the correct answer is 13824. The option 13834 results from an error in the final multiplication. Exam tip: to find a cube, first square the number and then multiply by the number once more.

The square of a number is obtained by multiplying it by itself: \(43^2 = 43 \times 43 = 1849\). Therefore, 1849 is correct. A value such as 1839 may result from a small multiplication error, but it is not the square of 43. Exam tip: You can quickly verify it using \((40+3)^2 = 40^2 + 2\times40\times3 + 3^2\).

An exponent of 3 means that 25 is multiplied by itself three times: \(25^3=25\times25\times25\). First, \(25\times25=625\), and then \(625\times25=15625\). Therefore, 15625 is correct. A value such as 14625 can result from an arithmetic error during multiplication. Exam tip: to find a cube, first find the square and then multiply it by the same number.

\(44^2=(40+4)^2=40^2+2\cdot40\cdot4+4^2=1600+320+16=1936\). Hence the correct value is 1936. The nearest distractors 1926 and 1946 are off by 10, while 1956 is off by 20, so they are incorrect. Exam tip: use the \((a+b)^2\) expansion for quick mental squaring of two-digit numbers or memorize squares up to 50.

An exponent of 3 means multiplying 26 by itself three times: \(26^3=26\times26\times26\). First, \(26\times26=676\), and then \(676\times26=17576\). Therefore, the correct answer is 17576. A value such as 16576 can result from an arithmetic error in multiplication. Exam tip: to find a cube, first find the square and then multiply it by the original number.

Here, \(45^2\) means \(45 \times 45\). Therefore, \(45 \times 45 = 2025\), so 2025 is correct. 2015 is not the square of 45 and may result from an arithmetic error in multiplication. Exam tip: To find the square of a number, multiply it by itself.

The exponent 3 means that 27 is multiplied by itself three times: \(27^3=27\times27\times27\). First, \(27\times27=729\), and then \(729\times27=19683\). Therefore, 19683 is correct. A value such as 18683 can result from an arithmetic error during multiplication. In exams, write a power as repeated multiplication to check the calculation.

46^2 = 46×46. Break the multiplication: 40×46 = 1840 and 6×46 = 276, so 1840+276 = 2116. Options A and B differ by ±10 (2106 and 2126) and represent common small arithmetic mistakes. Exam tip: use distributive splitting (e.g., 46=(40+6)) to compute squares mentally and avoid errors.

An exponent of 3 means multiplying 28 by itself three times: \(28^3=28\times28\times28\). First, \(28\times28=784\), and then \(784\times28=21952\). Therefore, the correct answer is 21952. A value such as 20952 can result from an arithmetic error in multiplication. Exam tip: to find a cube, first find the square of the number and multiply it by the same number.

\(47^2\) means \(47 \times 47\). Since \(47 \times 47 = 2209\), the correct answer is 2209. Although 2199 is close, it is not the square of 47. Exam tip: use \((50-3)^2 = 2500-300+9 = 2209\) to calculate the square quickly.

An exponent of 3 means multiplying 29 by itself three times: \(29^3=29\times29\times29\). First, \(29\times29=841\), and then \(841\times29=24389\). Therefore, 24389 is correct. A value such as 23389 can result from an arithmetic error in multiplication. Exam tip: to find a cube, first square the number and then multiply by the number once more.