Exponents

Here, 6^3 = 6 × 6 × 6 = 216 and 2^4 = 2 × 2 × 2 × 2 = 16. Therefore, 6^3 - 2^4 = 216 - 16 = 200, so option B is correct. A value such as 210 can result from evaluating 2^4 incorrectly. Exam tip: calculate each power separately before performing subtraction.

When powers with the same base are divided, subtract the exponents: \(8^3 \div 8^2 = 8^{3-2}=8^1=8\). Therefore, the correct answer is 8. The value would be 1 only if the exponents were equal, such as \(8^2 \div 8^2\). Exam tip: for division with the same base, subtract the exponents.

Given \(a^3=343\). Since \(7^3=7\times7\times7=343\), we get \(a=7\). Option 8 is not correct because \(8^3=512\). Exam tip: Remember that \(343\) is the cube of \(7\).

Compute the powers first: \(9^2=81\) and \(4^3=64\). Adding these gives \(81+64=145\), so 145 is correct. Option A (93) is a common mistake from treating \(4^3\) as \(4\times3=12\). Exam tip: always evaluate exponents before performing addition or other operations.

Here, \(10^3 = 10 \times 10 \times 10 = 1000\). Therefore, \(1000 - 400 = 600\), so option D is correct. The value 700 would result from subtracting only 300 from 1000. Exam tip: evaluate the exponent first, then perform addition or subtraction.

Evaluate the exponent first: \(12^2=144\). Then \(144+25=169\), so the correct answer is 169. A value such as 159 usually results from an error in squaring or addition. Exam tip: In expressions with mixed operations, evaluate exponents first.

Evaluate the exponent first: \(13^2=13\times13=169\). Then \(169-69=100\), so 100 is the correct answer. A result such as 95 can arise from an error in subtraction. Exam tip: calculate powers before performing addition or subtraction.

First evaluate the exponent: \(14^2=14\times14=196\). Adding 14 gives \(196+14=210\). Therefore, 210 is correct. The close distractor 196 is only the value of \(14^2\); the additional 14 has not been included. Exam tip: evaluate exponents before carrying out the remaining operations.

When powers with the same base are divided, subtract their exponents: \(15^2 \div 15^1 = 15^{2-1}=15^1=15\). Therefore, 15 is correct. \(225\) is only the value of \(15^2\); it does not account for division by \(15^1\). Exam tip: use \(a^m \div a^n=a^{m-n}\) for the same base.

Given \(b^2=256\), we get \(b=\pm\sqrt{256}=\pm16\). Since the question asks for the positive value of \(b\), the correct answer is \(16\). Although 18 is close, \(18^2=324\), not 256. Exam tip: A squared variable can have two values, but choose the positive square root when a positive value is asked.

Compute each square: \(16^2=256\) and \(17^2=289\). Adding gives \(256+289=545\). As a quick check use the identity \((a+b)^2-2ab\): \((16+17)^2-2\cdot16\cdot17=33^2-544=1089-544=545\). Close options like 535 or 555 result from simple addition/subtraction mistakes. Exam tip: memorize small squares and use the identity \((a+b)^2-2ab\) to verify sums of squares quickly.

First evaluate the exponent: \(17^2=17\times17=289\). Then \(289-89=200\), so the correct answer is \(200\). The option \(210\) may result from an error in subtraction. Exam tip: In a mixed expression, evaluate exponents before addition or subtraction.

Any non-zero number raised to the power 0 equals 1, so \(18^0=1\). Therefore, \(18^2 \div 18^0=324 \div 1=324\). Option 1 is only the value of \(18^0\), not of the complete expression. Exam tip: before applying the zero-exponent rule, check that the base is non-zero.

First evaluate the exponent: \(20^2=20\times20=400\). Then \(400-100=300\). Therefore, the correct answer is 300. A value such as 350 can result from an error in subtraction. Exam tip: In an expression with brackets, evaluate the exponent before performing subtraction.

Since \(10^3=10\times10\times10=1000\), \(c=10\). Although 9 is close, \(9^3=729\), not 1000. Exam tip: find or verify the cube root of the given number in such questions.

Evaluate the exponent first: \(22^2 = 484\). Then add: \(484 + 32 = 516\). Thus the correct value is 516. The distractors (506, 526, 496) do not match this sum — for example 506 would result from subtracting 10 by mistake. Exam tip: compute squares quickly using expansion, e.g. \((20+2)^2 = 20^2 + 2\times20\times2 + 2^2\).

First evaluate the exponent: \(23^2=23\times23=529\). Then \(529-129=400\), so the correct answer is 400. The value 529 is only \(23^2\); 129 must still be subtracted. Exam tip: evaluate exponents before performing subtraction in such expressions.

Here, 24 can be written as \(24^1\). When powers with the same base are divided, their exponents are subtracted: \(24^2 \div 24^1=24^{2-1}=24\). Therefore, the correct answer is 24. The value 576 is \(24^2\), but the expression also requires division by 24. Exam tip: for division of powers with the same base, subtract the exponents.

First evaluate the exponent: \(25^2=25\times25=625\). Adding 100 gives \(625+100=725\). Therefore, the correct answer is 725. The value 625 is only \(25^2\); it does not include the added 100. Exam tip: Under BODMAS, evaluate exponents before addition or subtraction.

First evaluate the exponent: \(26^2=26\times26=676\). Then \(676-76=600\), so 600 is the correct answer. A value such as 590 may result from an error in subtraction. Exam tip: In a mixed expression, evaluate exponents before addition or subtraction.