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Unit 6.3 Product, Power and Quotient Rule

See Unit 5.1 for a refresher on exponents

Product Rule

To multiply two values with the same bases but different fractional exponents, you first need to find a common denominator for the exponents and then add them

Product Rule

[latex]2^{\frac{1}{2}} \times 2^{\frac{1}{3}} = 2^{\frac{1}{2} + \frac{1}{3}} = 2^{\frac{3}{6} + \frac{2}{6}} = 2^{\frac{5}{6}}[/latex]

Quotient Rule

To divide two values with the same bases but different fractional exponents, you first need to find a common denominator for the exponents and then subtract them

Quotient Rule

[latex]\frac{2^{\frac{1}{2}}}{2^{\frac{1}{3}}} = 2^{\frac{1}{2} - \frac{1}{3}} = 2^{\frac{3}{6} - \frac{2}{6}} = 2^{\frac{1}{6}}[/latex]

Power Rule

When you have a power to a power, multiply the powers

Power Rule

[latex]\left( 9^{\frac{1}{2}} \right)^2 = 9^{\frac{1 \cdot 2}{2}} = 9^1 = 9[/latex]

 

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ESET1140: Intermediate Technical Algebra Copyright © 2024 by froenico. All Rights Reserved.