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SubjectsMathematics
घातांक
In Class 9 Mathematics, the topic Exponents builds on Number Systems by showing how repeated multiplication is represented compactly using powers. Students learn to identify the base and exponent, apply the laws of exponents while multiplying and dividing powers, and work with zero and negative integral exponents. They practise simplifying numerical and algebraic expressions, compare powers, and use exponent notation accurately to express very large or very small numbers.
TOPIC PRACTICE
Up to 25 questions from this page. Select your focus, then start.
First evaluate the powers: \(12^3=1728\) and \(12^2=144\). Therefore, \(12^3-12^2=1728-144=1584\), so option A is correct. In an exam, calculate the two powers separately before performing the subtraction.
Evaluate the powers first: 19^2 = 19 × 19 = 361 and 8^3 = 8 × 8 × 8 = 512. Therefore, 19^2 + 8^3 = 361 + 512 = 873, so option B is correct. In an exam, calculate each power separately before performing the final addition to avoid arithmetic errors.
Given \(e^2=1849\), the positive value of \(e\) is the positive square root of 1849. Since \(43^2=43\times43=1849\), we get \(e=43\). The closest distractor, 42, is incorrect because \(42^2=1764\), not 1849. Exam tip: when a variable has a positive square value, check the positive integer whose square equals the given number.
Compute powers first: \(20^2=400\) and \(9^3=729\). Adding gives \(400+729=1129\), so 1129 is correct. The closest distractor C (1128) likely comes from misreading \(9^3\) as 728 or a one-unit arithmetic slip, so it is incorrect. Exam tip: evaluate each power separately, then add and quickly check the units digit for a sanity check.
For division of powers with the same base, use \(a^m \div a^n=a^{m-n}\). Thus, \(13^5 \div 13^4=13^{5-4}=13^1=13\). Therefore, option A is correct. Remember that exponents are subtracted when dividing like bases, not multiplied; hence 169, which is \(13^2\), is not the answer.
Evaluate the powers first: 21^2 = 21 × 21 = 441 and 10^3 = 10 × 10 × 10 = 1000. Therefore, 21^2 + 10^3 = 441 + 1000 = 1441, so option B is correct. In an exam, calculate each power separately before performing the addition.
Evaluate the powers first: \(2^8=256\) and \(3^7=2187\). Therefore, \(2^8+3^7=256+2187=2443\), so option C is correct. In an exam, calculate each power separately before performing the addition to avoid place-value errors.
Compute each power separately. \(22^2=22\times22=484\) and \(11^3=11\times11\times11=11\times121=1331\). Adding gives \(484+1331=1815\). Option B (1805) is wrong — it likely comes from a small arithmetic slip when computing the cube or the final addition. Exam tip: calculate powers one at a time and verify by checking last digits or re-adding to catch simple mistakes.
Given \(f^3=13824\). Since \(24^3=24\times24\times24=13824\), it follows that \(f=24\). The cubes of the other options are not equal to 13824. Exam tip: When the cube of a number is given, find its cube root and verify the answer by cubing it again.
Using the power-of-a-power rule, (a^m)^n = a^{mn}. Therefore, ((6^3)^2) = 6^{3×2} = 6^6 = 46656. Hence, 46656 is correct. Exam tip: when a power is raised to another power, multiply the exponents rather than adding them.
Evaluate the powers first: \(23^2=23\times23=529\) and \(12^3=12 imes12 imes12=1728\). Therefore, \(23^2+12^3=529+1728=2257\), so option C is correct. As an exam tip, calculate each exponent separately before performing the addition; adding the bases would be incorrect.
Compute the powers separately: \(24^2=576\) and \(13^3=2197\). Adding gives \(576+2197=2773\), so the correct value is 2773. The close distractor 2783 is incorrect — it reflects a typical addition or cube-miscalculation error (e.g. treating 2197 as 2207). Exam tip: calculate each power first and then add; memorise small squares and cubes to avoid simple mistakes.
For division of powers with the same base, subtract the exponents: \(a^m \div a^n=a^{m-n}\). Therefore, \(14^4 \div 14^2=14^{4-2}=14^2=196\). Option B, \(14^3\), would result only if the exponent difference were 3. Exam tip: subtract exponents for division with the same base and add them for multiplication.
Evaluate the powers first: 25^2 = 625 and 14^3 = 14 × 14 × 14 = 2744. Therefore, 25^2 + 14^3 = 625 + 2744 = 3369, so option B is correct. Exam tip: Calculate each exponent separately before performing the addition to avoid arithmetic errors.
Since \(45^2=45\times45=2025\), the positive value satisfying \(g^2=2025\) is \(g=45\). The equation has two real solutions, \(g=45\) and \(g=-45\), but the question specifically asks for the positive value. Exam tip: when the positive square root is requested, choose the principal square root.
Compute the powers first: \(26^2=676\) and \(15^3=3375\). Adding them gives \(676+3375=4051\), so 4051 is correct. The closest distractor 4041 likely results from a simple addition error (for example mis-adding by 10). Exam tip: evaluate each power separately, add using place value columns, and recheck the final addition to avoid small arithmetic mistakes.
For division of powers with the same base, use \(a^m \div a^n = a^{m-n}\). Thus, \(15^5 \div 15^4 = 15^{5-4} = 15^1 = 15\). Therefore, option A is correct. Remember that exponents are subtracted during division, not multiplied.
Evaluate the powers first: 27^2 = 27 × 27 = 729 and 16^3 = 16 × 16 × 16 = 4096. Therefore, 27^2 + 16^3 = 729 + 4096 = 4825, so option B is correct. Exam tip: calculate each power separately before performing the addition to avoid confusing exponentiation with addition.
When powers with the same base are divided, their exponents are subtracted: \(a^m \div a^n=a^{m-n}\). Therefore, \(5^7 \div 5^4=5^{7-4}=5^3=125\), so option C is correct. Exam tip: For division with the same base, subtract the exponents rather than multiplying them.
Compute the powers first: \(28^2 = 784\) and \(17^3 = 4913\). Adding them gives \(784 + 4913 = 5697\). The closest distractor 5687 would result from mistakenly taking \(17^3=4903\) (10 less), while 5707 could come from adding an extra 10. Exam tip: evaluate each power separately and then add; use the units digit check (4+3=7) to quickly verify the last digit of the sum.
Evaluate the powers first: 16^3 = 4096 and 16^2 = 256. Therefore, 16^3 - 16^2 = 4096 - 256 = 3840, so option A is correct. Exam tip: calculate both powers before subtracting; 4096 is only the value of 16^3, not of the complete expression.
We are given \(h^3=15625\). Since \(25^3=25\times25\times25=15625\), it follows that \(h=25\). The cubes of the other options are not equal to 15625. Exam tip: When the cube of a number is given, find its cube root and verify the result by cubing it.
For division of powers with the same base, subtract the exponents: \(18^3 \div 18^2 = 18^{3-2} = 18^1 = 18\). Therefore, option A is correct. The answer 324 results from applying an incorrect operation instead of subtracting the exponents. Exam tip: add exponents when multiplying like bases and subtract them when dividing like bases.
Evaluate the powers first: 29^2 = 841 and 18^3 = 18 × 18 × 18 = 5832. Therefore, 841 + 5832 = 6673, so option B is correct. In such questions, calculate each power separately before performing the addition.
Use the power-of-a-power rule: \((a^m)^n = a^{mn}\). Therefore \((7^2)^3 = 7^{2\times3} = 7^6 = 117649\). Option A (16807) equals \(7^5\), B (823543) equals \(7^7\), and D (2401) equals \(7^4\), so they are incorrect. Exam tip: multiply the exponents first for expressions of the form \((a^m)^n\).
QUIZ COMPLETE
