Mathematics

Laws of Exponents

Q: Which of the following rules correctly describes the division of powers with the same base?

\(\frac{a^m}{a^n}=a^{m-n}\), \(a\ne0\) When powers have the same non-zero base, their exponents are subtracted: \(a^m/a^n=a^{m-n}\). Option A is the multiplication rule. Exam tip: a division sign signals subtraction of exponents.

Q: If \(x\ne 0\), what is the simplified form of \(\frac{x^6}{x^2}\)?

\(x^4\) When powers with the same base are divided, their exponents are subtracted: \(\frac{x^m}{x^n}=x^{m-n}\). Therefore, \(\frac{x^6}{x^2}=x^{6-2}=x^4\). In option B, the exponents have been added, which is the rule for multiplication, not division. Exam tip: subtract exponents in division and add them in multiplication when the bases are the same.

Q: What is the value of \(x^0\) when \(x\ne 0\)?

\(1\) By the laws of exponents, the zero power of any non-zero number or variable is 1. Therefore, \(x^0=1\) for \(x\ne 0\). Option C is incorrect because it represents the base \(x\), not the value of its zero power. Exam tip: the zero power of every non-zero base is always 1.

This Class 9 Mathematics topic explains how to work confidently with powers and exponents through the key laws of exponents. Students learn to multiply and divide powers with the same base, raise a power to another power, handle zero and negative exponents, and simplify numerical or algebraic expressions correctly. Presented under Common Questions, it also helps learners understand why each rule works, avoid common sign and base errors, and apply exponent laws while solving routine problems.

Easy · Level 1 · 3 questions

Practice questions

01Which of the following rules correctly describes the division of powers with the same base?

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Answer and explanation

Correct answer: B. \(\frac{a^m}{a^n}=a^{m-n}\), \(a\ne0\)

When powers have the same non-zero base, their exponents are subtracted: \(a^m/a^n=a^{m-n}\). Option A is the multiplication rule. Exam tip: a division sign signals subtraction of exponents.

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02If \(x\ne 0\), what is the simplified form of \(\frac{x^6}{x^2}\)?

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Answer and explanation

Correct answer: A. \(x^4\)

When powers with the same base are divided, their exponents are subtracted: \(\frac{x^m}{x^n}=x^{m-n}\). Therefore, \(\frac{x^6}{x^2}=x^{6-2}=x^4\). In option B, the exponents have been added, which is the rule for multiplication, not division. Exam tip: subtract exponents in division and add them in multiplication when the bases are the same.

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03What is the value of \(x^0\) when \(x\ne 0\)?

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Answer and explanation

Correct answer: B. \(1\)

By the laws of exponents, the zero power of any non-zero number or variable is 1. Therefore, \(x^0=1\) for \(x\ne 0\). Option C is incorrect because it represents the base \(x\), not the value of its zero power. Exam tip: the zero power of every non-zero base is always 1.

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Laws of Exponents

Practice questions

01Which of the following rules correctly describes the division of powers with the same base?निम्नलिखित में से कौन-सा नियम समान आधार वाली घातों के भाग का सही वर्णन करता है?

02If \(x\ne 0\), what is the simplified form of \(\frac{x^6}{x^2}\)?यदि \(x\ne 0\), तो \(\frac{x^6}{x^2}\) का सरल रूप क्या है?

03What is the value of \(x^0\) when \(x\ne 0\)?जब \(x\ne 0\) हो, तब \(x^0\) का मान क्या होगा?

Analytics choices

01Which of the following rules correctly describes the division of powers with the same base?

02If \(x\ne 0\), what is the simplified form of \(\frac{x^6}{x^2}\)?

03What is the value of \(x^0\) when \(x\ne 0\)?