MathematicsChapter 2: Logarithms
Product and Quotient
For powers of the same base, a^m x a^n = a^(m+n) and a^m / a^n = a^(m-n).
Learning objectives
- Define and explain product and quotient.
- Apply product and quotient to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Definition
For powers of the same base, a^m x a^n = a^(m+n) and a^m / a^n = a^(m-n). In scientific notation you first multiply or divide the d parts, then add or subtract the n parts. If d becomes 12, rewrite 12 x 10^k as 1.2 x 10^(k+1). If d becomes 0.6, rewrite as 6.0 x 10^(k-1).
Formula
n = a(m+n) and am / an
Where / symbols
- Product And Quotient
- For powers of the same base, a^m x a^n = a^(m+n) and a^m / a^n = a^(m-n). In scientific notation you first multiply or divide the d parts, then add or subtract the n parts. If d becomes 12, rewrite 12 x 10^k as 1.2 x 10^(k+1). If d becomes 0.6, rewrite as 6.0 x 10^(k-1).
Overview
Learn the idea, then use it:
Core Understanding
For powers of the same base, a^m x a^n = a^(m+n) and a^m / a^n = a^(m-n). In scientific notation you first multiply or divide the d parts, then add or subtract the n parts. If d becomes 12, rewrite 12 x 10^k as 1.2 x 10^(k+1). If d becomes 0.6, rewrite as 6.0 x 10^(k-1).
Examples add · subtract · Multiply · PRODUCT AND QUOTIENT: For powers of the same base, a^m x a^n = a^(m+n) and a^m / a^n = a^(m-n). In scientific notation you first multiply or d
Exam Application
State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.
Examples Define first · Show the rule or evidence · Check units, labels, and conclusion
WHAT — PRODUCT AND QUOTIENT
For powers of the same base, a^m x a^n = a^(m+n) and a^m / a^n = a^(m-n). In scientific notation you first multiply or divide the d parts, then add or subtract the n parts. If d becomes 12, rewrite 12 x 10^k as 1.2 x 10^(k+1). If d becomes 0.6, rewrite as 6.0 x 10^(k-1).
HOW — Use the idea
Identify what is given, select this topic's rule or evidence, apply it one step at a time, and check the result.
In simple words
Do not merge product and quotient with a neighbouring idea that uses a different definition, rule, or method.
Key points
- add
- subtract
- Multiply
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Product and Quotient
Sticky Notes · Quick Revision
Core Idea
- For powers of the same base, a^m x a^n = a^(m+n) and a^m / a^n = a^(m-n).
Key Points
- add
- subtract
- Multiply
Simple Check
- Explain product and quotient in your own words and connect it to one chapter example.
How to Answer
- Define the idea, show the main rule or evidence, apply it, and check the final statement.
Common Mistake
- Do not merge product and quotient with a neighbouring idea that uses a different definition, rule, or method.
FBISE Exam Tip
- Use the exact term, show working where needed, and include units or labelled evidence.
60-second revision
- For powers of the same base, a^m x a^n = a^(m+n) and a^m / a^n = a^(m-n).
- add
- subtract
- Multiply
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