Laws of Exponents

Scientific Notation

Summary of Laws of Exponents

1. b^m · bⁿ = b ^{(m + n)}  
2. b^m ÷ bⁿ = b^{(m – n)} where m ≥ n and b ≠ 0.
   (In Session 41, we will extend this property to values with m < n.)
3. a⁰ = 1, when a ≠ 0
4. (b^m)ⁿ = b^mn
5. (ab)ⁿ = aⁿbⁿ    

We are now able to answer the astronomer's problem given on page 2 of this session.

An astronomer studying a region of space needs to determine the volume of a cubic region whose edges measure 3 × 10⁸ miles long. Find the volume of that region of space.

The cubic region of space has a volume of 2.7 × 10²⁵ cubic miles.

Self-Check Problem

Use the Laws of Exponents to simplify the expression (2a⁶b)³(3a²b³)².

Solution

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