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]