What is simplified form of (\frac{x^m}{x^n} \cdot x^p)
Answer and explanation
Correct answer: x^{m-n+p}
Using the laws of exponents, division of like bases gives \(x^m/x^n=x^{m-n}\). Multiplication of like bases then adds the exponents, so \(x^{m-n}\cdot x^p=x^{m-n+p}\). Option C incorrectly adds the exponents in the quotient, while option D uses the wrong sign for \(p\). This simplification is valid for \(x\neq0\). Exam tip: subtract exponents when dividing like bases and add them when multiplying like bases.
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What is the correct answer to this question?
x^{m-n+p}
Why is this the correct answer?
Using the laws of exponents, division of like bases gives \(x^m/x^n=x^{m-n}\). Multiplication of like bases then adds the exponents, so \(x^{m-n}\cdot x^p=x^{m-n+p}\). Option C incorrectly adds the exponents in the quotient, while option D uses the wrong sign for \(p\). This simplification is valid for \(x\neq0\). Exam tip: subtract exponents when dividing like bases and add them when multiplying like bases.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Exponents.
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