Answer:
[tex](\frac{6}{10})^3 * (\frac{5}{9})^2 = \frac{1}{15}[/tex]
Step-by-step explanation:
Given
[tex](\frac{6}{10})^3 * (\frac{5}{9})^2[/tex]
Required
Solve:
[tex](\frac{6}{10})^3 * (\frac{5}{9})^2[/tex]
Simplify 6/10
[tex](\frac{6}{10})^3 * (\frac{5}{9})^2 = (\frac{3}{5})^3 * (\frac{5}{9})^2[/tex]
Express 9 as 3^2
[tex](\frac{6}{10})^3 * (\frac{5}{9})^2 = (\frac{3}{5})^3 * (\frac{5}{3^2})^2[/tex]
Apply law of indices
[tex](\frac{6}{10})^3 * (\frac{5}{9})^2 = \frac{3^3}{5^3}* \frac{5^2}{(3^2)^2}[/tex]
[tex](\frac{6}{10})^3 * (\frac{5}{9})^2 = \frac{3^3}{5^3}* \frac{5^2}{3^4}[/tex]
Express as a sing;e fraction
[tex](\frac{6}{10})^3 * (\frac{5}{9})^2 = \frac{3^3*5^2}{5^3*3^4}[/tex]
Apply law of indices:
[tex](\frac{6}{10})^3 * (\frac{5}{9})^2 = \frac{1}{5^{3-2}*3^{4-3}}[/tex]
[tex](\frac{6}{10})^3 * (\frac{5}{9})^2 = \frac{1}{5^1*3^1}[/tex]
[tex](\frac{6}{10})^3 * (\frac{5}{9})^2 = \frac{1}{5*3}[/tex]
[tex](\frac{6}{10})^3 * (\frac{5}{9})^2 = \frac{1}{15}[/tex]
