Division rule for indices

Division Rule for Indices

Introduction

• Indices, also known as powers or exponents, are used to represent a number that has been multiplied by itself.
• The division rule is one of the fundamental rules in the laws of indices and applies when dividing terms with the same base.

Division Rule Explained

• When you divide two numbers with the same base and different indices, the outcome is the base with an index equal to the difference of the original indices.
• The division rule is expressed as: a^m / a^n = a^(m-n)

Parts of the Division Rule

• a is the base of the terms being divided.
• m and n are the indices of the terms.
• m-n is the new power or exponent of the base after the division has been carried out.

Usage of the Division Rule

• The division rule for indices simplifies the division of terms with the same base but different powers.
• This law is particularly useful when simplifying algebraic expressions or solving equations.

Examples

• For an example, a^6 / a^3 = a^(6-3) = a^3.
• As another example, b^8 / b^5 = b^(8-5) = b^3.

Conclusion

• A sound understanding of the division rule for indices is important when performing algebraic manipulations.
• This rule, like other rules for indices, plays a central role in algebra and is often foundational for more advanced mathematical topics. Regular practice with the division rule will ensure increased familiarity and fluidity in mathematics problems.