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Common mistakes made when solving the Exponent and Power problemsThough the students enjoy solving the exponents and power problems, however in many cases they tend to make mistakes. These mistakes could be out of carelessness or because the child did not under the concept properly. It is always a good idea to be aware about the common mistakes which students make so that it can be corrected from the early age. Here are some of the common mistakes which students usually make when solving the exponents and power problems.☞ a^{m}+a^{n}=a^{m+n}We will try to understand this by an example.2^{3}+2^{4}≠2^{7} In this case LHS is not same as RHS. Ways to teach the children to minimize this error 2^{3} means multiplying 2 by itself 3 times (2×2×2) 2^{4} means multiplying 2 by itself 4 times (2×2×2×2) 2^{7} means multiplying 2 by itself 7 times (2×2×2×2×2×2×2). So the LHS is (2×2×2)+(2×2×2×2) and RHS is (2×2×2)×(2×2×2×2). LHS is NOT same as RHS. ☞ a^{m}−a^{n}=a^{m−n}We will try to understand this by an example.3^{4}−3^{2}≠3^{2} In this case LHS is not same as RHS. Ways to teach the children to minimize this error 3^{4} means multiplying 3 by itself 4 times (3×3×3×3) 3^{2} means multiplying 3 by itself 2 times (3×3) 3^{2} means multiplying 3 by itself 2 times (3×3) So the LHS is (3×3×3×3)−(3×3) and RHS is (3×3). LHS is NOT same as RHS. ☞ a^{m}×a^{n}=a^{m×n}We will try to understand this by an example.5^{3}×5^{2}≠5^{6} In this case LHS is not same as RHS. Ways to teach the children to minimize this error 5^{3} means multiplying 5 by itself 3 times (5×5×5) 5^{2} means multiplying 5 by itself 2 times (5×5) 5^{6} means multiplying 5 by itself 6 times (5×5×5×5×5×5) So the LHS is (5×5×5)×(5×5) and RHS is (5×5×5×5×5×5). LHS is NOT same as RHS. ☞ a^{m}÷a^{n}=a^{m÷n}We will try to understand this by an example.10^{6}÷10^{3}≠10^{2} In this case LHS is not same as RHS. Ways to teach the children to minimize this error 10^{6} means multiplying 10 by itself 6 times (10×10×10×10×10×10) 10^{3} means multiplying 10 by itself 3 times (10×10×10) 10^{2} means multiplying 10 by itself 2 times (10×10) So the LHS is (10×10×10×10×10×10)÷(10×10×10) and RHS is (10×10). LHS is NOT same as RHS. The best way to remove the above confusion and to ensure the children have less chance of committing mistakes is to practice the problems related to the above situations. Click on Exponents & Power to practice. We will be happy to hear from you. To leave a feedback or share your experience about any type of mistake made while solving Math problem, please click My Comment. Given below are other commonly made mistakes in Math: Clock Reading Time | Exponents & Power | Whole to number-word | Square root | Lines & Angles | Integers | Area Plane Figure | Perimeter Plane Figure | Algebraic Identities | Congruence of Triangles | Similar Triangles | Coordinate Geometry | Trigonometry | Solving equations | Polynomial | Division | Algebraic Expression | Average | |
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