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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.
Correct answer: A. 91125
Explanation: An exponent of 3 means that 45 is multiplied by itself three times: \(45^3=45\times45\times45\). First, \(45\times45=2025\), and then \(2025\times45=91125\). Therefore, the correct answer is 91125. Note that 2025 is the value of \(45^2\), not \(45^3\). Exam tip: To find a cube, first find the square and then multiply it by the original number.
Correct answer: A. Three
Explanation: The governing concept is the inverse relationship between cubing and taking a cube root. Let the positive number be x. Then x³ = 27. Since 27 = 3 × 3 × 3 = 3³, taking the positive cube root gives x = 3. The distractors do not work: 9³ = 729, while 27³ and 81³ are much larger than 27. Therefore, option A is correct.
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