Exponents

First evaluate the exponent: \(33^2 = 33 \times 33 = 1089\). Then \(1089 - 489 = 600\). Therefore, the correct answer is 600. The value 1089 is only \(33^2\); the subtraction of 489 must still be performed. Exam tip: In a mixed expression, evaluate exponents before addition or subtraction.

Since the square root of 324 is 18, the possible values of d are 18 and -18. As the question asks for the positive value, d = 18 is correct. Option 16 is not correct because 16² = 256, not 324. Exam tip: When the positive value is asked in d² = n, take the positive square root of n.

First find the square of 35: 35² = 1225. Adding 25 gives 1225 + 25 = 1250. Therefore, 1250 is the correct answer. Option 1225 is only the value of 35²; it does not include the added 25. Exam tip: evaluate the exponent first, then perform addition or subtraction.

First find the square of 36: \(36^2=36\times36=1296\). Then \(1296-696=600\), so the correct answer is 600. The option 650 can result from an error in subtraction. Exam tip: after finding a square, verify the subtraction using column subtraction or a quick mental check.

Evaluate the powers first: \(2^6=64\) and \(3^3=27\). Therefore, \(2^6+3^3=64+27=91\). Hence, 91 is the correct answer. An option such as 81 does not result from correctly evaluating and adding both powers. Exam tip: In such expressions, calculate exponents before performing addition or subtraction.

Given x^3=512. Since 8^3=8×8×8=512, x=8. Option 7 is not correct because 7^3=343. Exam tip: Memorising cubes of numbers from 1 to 10 helps solve such questions quickly.

First find the square of 38: \(38^2=38\times38=1444\). Then, \(1444-444=1000\), so the correct answer is 1000. An answer such as 900 can result from an error in finding the square or in subtraction. Exam tip: In an expression with brackets, evaluate the exponent (square) before performing subtraction.

When powers with the same base are divided, subtract the exponents: \(7^4 \div 7^2 = 7^{4-2} = 7^2 = 49\). Therefore, 49 is correct. 343 is \(7^3\), so it does not result here. Exam tip: use \(a^m \div a^n = a^{m-n}\) only when the non-zero bases are the same.

First evaluate the exponent: \(40^2 = 40 \times 40 = 1600\). Then \(1600 - 600 = 1000\). Therefore, the correct answer is 1000. An option such as 1100 may result from an error in subtraction. Exam tip: In an expression with brackets, calculate the exponent before performing subtraction.

Since 21 × 21 = 441, the positive square root of 441 is 21. Although the equation y² = 441 has two solutions, 21 and −21, the question asks for the positive value, so 21 is correct. The close distractor 19 is incorrect because 19² = 361. Exam tip: when the positive value is asked in y² = a, take √a.

Compute powers: \(4^5=1024\) and \(4^2=16\), so \(1024-16=1008\). Why other options are wrong: 1024 corresponds to forgetting the subtraction step; 16 is just \(4^2\) alone; 1000 is a rounded estimate. Exam tip: factor out \(4^2\): \(4^5-4^2=4^2(4^3-1)=16(64-1)=16\times63=1008\), which helps avoid large subtraction errors.

First find the square of 42: 42² = 1764. Subtracting 764 from 1764 gives 1000. Therefore, the correct answer is 1000. An option such as 1100 may result from an error in subtraction at the hundreds place. Exam tip: In an expression with exponents, evaluate the exponent first and then perform addition or subtraction.

When powers with the same base are divided, subtract their exponents: \(9^4 \div 9^2 = 9^{4-2}=9^2=81\). Therefore, 81 is correct. The option 9 is only \(9^1\), so it is not correct. Exam tip: use \(a^m \div a^n=a^{m-n}\), where \(a\ne0\).

Since 9 × 9 × 9 = 729, we get z = 9. The cube of 8 is 512, so 8 is not correct. Exam tip: verify a perfect cube by multiplying the number by itself three times.

First find the square of 44: \(44^2=1936\). Then \(1936-936=1000\). Therefore, the correct answer is 1000. Option 900 may result from an error in subtraction. Exam tip: evaluate exponents before performing addition or subtraction.

Here, \(2^3=2\times2\times2=8\) and \(3^2=3\times3=9\). Therefore, \(2^3\times3^2=8\times9=72\). Option 64 is the value of \(2^6\), so it is not correct. Exam tip: Evaluate each exponential term separately before multiplying.

Evaluate the powers first: 2^6 = 64 and 2^3 = 8. Therefore, 64 + 8 = 72, so 72 is correct. The option 64 is only the value of 2^6; it does not include the addition of 2^3. Exam tip: In an expression with exponents, evaluate each power before performing addition or subtraction.

Here, 3^5 = 243 and 3^2 = 9. Therefore, 3^5 - 3^2 = 243 - 9 = 234. Hence, option B is correct. The value 244 may result from an incorrect subtraction by 10. Exam tip: Evaluate each power separately before performing subtraction.

When powers with the same base are divided, subtract the exponents: \(4^4 \div 4^2 = 4^{4-2} = 4^2 = 16\). Therefore, 16 is the correct answer. 64 equals \(4^3\), which may result from subtracting the exponents incorrectly. Exam tip: use \(a^m \div a^n = a^{m-n}\), where \(a \ne 0\).

Given \(x^2=196\), we get \(x=\pm\sqrt{196}=\pm14\). Since the question asks for the positive value of \(x\), the answer is \(14\). The close distractor \(12\) is incorrect because \(12^2=144\), not 196. Exam tip: For \(x^2=a\), there are usually two values, \(\pm\sqrt a\); select only the positive one when asked.