Answer:
[tex](\frac{3}{4})^3 * (\frac{2}{3})^2 = \frac{3}{16}[/tex]
Step-by-step explanation:
Given
[tex](\frac{3}{4})^3 * (\frac{2}{3})^2[/tex]
Required
Solve:
[tex](\frac{3}{4})^3 * (\frac{2}{3})^2[/tex]
Apply law of indices
[tex](\frac{3}{4})^3 * (\frac{2}{3})^2 = \frac{3^3}{4^3} * \frac{2^2}{3^2}[/tex]
Express 4 as 2^2
[tex](\frac{3}{4})^3 * (\frac{2}{3})^2 = \frac{3^3}{(2^2)^3} * \frac{2^2}{3^2}[/tex]
[tex](\frac{3}{4})^3 * (\frac{2}{3})^2 = \frac{3^3}{2^6} * \frac{2^2}{3^2}[/tex]
Express as a singe fraction
[tex](\frac{3}{4})^3 * (\frac{2}{3})^2 = \frac{3^3*2^2}{2^6*3^2}[/tex]
Apply law of indices:
[tex](\frac{3}{4})^3 * (\frac{2}{3})^2 = \frac{3^{3-2}}{2^{6-2}}[/tex]
[tex](\frac{3}{4})^3 * (\frac{2}{3})^2 = \frac{3^1}{2^4}[/tex]
[tex](\frac{3}{4})^3 * (\frac{2}{3})^2 = \frac{3}{16}[/tex]
