Multiplication of Algebraic Fractions & Raising Fractions to a Power
Big Idea: Just as we multiply numerical fractions by multiplying numerators and denominators separately, we apply the same principle to algebraic fractions (rational expressions) — and then simplify by factoring.
0. Quick Numerical Review (30 seconds)
Recall: $\dfrac{2}{3} \times \dfrac{5}{7} = \dfrac{2 \times 5}{3 \times 7} = \dfrac{10}{21}$
And: $\left(\dfrac{2}{3}\right)^3 = \dfrac{2^3}{3^3} = \dfrac{8}{27}$
Now let's see how this works when the numerators and denominators contain variables.