Exponents

An exponent of 3 means that 6 is multiplied by itself three times: \(6^3=6\times6\times6=216\). Therefore, the correct answer is 216. The value 36 is \(6^2\), not \(6^3\). Exam tip: in \(a^n\), multiply the base \(a\) by itself \(n\) times.

When powers with the same base are multiplied, their exponents are added: \(2^3\times2^1=2^{3+1}=2^4=16\). Therefore, the correct answer is 16. The value 8 is only \(2^3\); it does not include multiplication by \(2^1\). Exam tip: use \(a^m\times a^n=a^{m+n}\) only when the bases are the same.

For any number, an exponent of 1 leaves the base unchanged: \(a^1=a\). Therefore, \(25^1=25\). Option 1 is the value of \(25^0\), while 625 equals \(25^2\). Exam tip: when the exponent is 1, write the base as it is.

The exponent 5 is a positive integer, so \(0^5=0\times0\times0\times0\times0=0\). Option 1 is associated with the rule \(a^0=1\), but that rule does not apply to \(0^5\); \(0^0\) is a separate case. Exam tip: Any positive power of zero is zero.

An exponent of 2 means the square of the number. Thus, \(17^2=17\times17=289\), so 289 is correct. The values 279, 299, and 269 are not obtained by multiplying 17 by 17. Exam tip: Check a square using direct multiplication or \((10+7)^2\).

An exponent of 3 means that 7 is multiplied by itself three times: \(7^3 = 7 \times 7 \times 7 = 343\). Therefore, 343 is correct. The value 392 comes from \(7 \times 7 \times 8\), so it is not \(7^3\). Exam tip: in \(a^3\), multiply the base \(a\) exactly three times.

Any number raised to the power 1 remains the same: \(a^1=a\). Therefore, \(100^1=100\). The value 1000 would result from multiplying 100 by 10, not from raising it to the power 1. Exam tip: when the exponent is 1, write the base directly.

An exponent of 2 means multiplying the number by itself. Thus, \(30^2 = 30 \times 30 = 900\). The option 300 may result from an incorrect place-value calculation instead of squaring 30. Exam tip: for a square, always multiply the number by itself.

An exponent of 4 means that 4 is multiplied by itself four times: \(4^4=4\times4\times4\times4=16\times16=256\). Therefore, 256 is correct. The value 64 is \(4^3\), so it is a close but incorrect option. Exam tip: in \(a^n\), n tells how many times a is used as a factor.

Any number raised to the power 1 remains unchanged: \(a^1=a\). Therefore, \(8^1=8\). The value \(64\) is \(8^2\), not \(8^1\). Exam tip: When the exponent is 1, the answer is the base itself.

Here, \(19^2\) means \(19 \times 19\). Since \(19 \times 19 = 361\), the correct answer is 361. The number 351 is not the square of 19. Exam tip: To find the square of a number, multiply the number by itself.

For every non-zero number \(a\), \(a^0=1\). Since 2 is non-zero, \(2^0=1\). Option 0 is incorrect because an exponent of zero does not mean multiplying the number by zero. Exam tip: use \(a^0=1\) only when \(a\ne0\).

When powers with the same base are multiplied, their exponents are added: \(3^2\times3^2=3^{2+2}=3^4=81\). Therefore, the correct answer is 81. The value 27 is \(3^3\), so it is not correct. Exam tip: Use \(a^m\times a^n=a^{m+n}\) only when the bases are the same.

Here, \(21^2\) means \(21\times 21\). Therefore, \(21\times 21=441\), so 441 is correct. 421 is not the square of 21. Exam tip: To find a square, multiply the number by itself.

In an exponent, 9^3 means multiplying 9 by itself three times: 9\times 9\times 9 = 81\times 9 = 729. Therefore, 729 is the correct answer. 819 may result from an incorrect multiplication rather than cubing 9. Exam tip: to find a^3, first calculate a^2 and then multiply it by a once more.

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.

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.

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.

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.

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.