The marked answer is correct.
[tex] \frac{64}{343} [/tex]
rules for exponents:
[tex] a^{0} = 1 \\ a^{1} =a \\ a^{n} * a^{m} = a^{n + m} \\ a^{n} / a^{m} = a^{n - m} \\ a^{n} * b^{n} = (a*b)^{n} \\ a^{n} / b^{n} = (a/b)^{n} \\ (a^{n}) ^{m} = a^{n*m} \\ b^{-n} = \frac{1}{ b^{n} } [/tex]
First step:
[tex] 6^{0} = 1[/tex]
Second step:
[tex] ( \frac{2^{2}}{7^{1}} ) ^{3} = \frac{ 2^{6} }{ 7^{3} } [/tex]
and
[tex] (1)^{3} = 1^{3} [/tex]
Last step:
[tex] 2^{6} * 1^3} = 64 * 1 = 64 \\ 7^{3} = 343 \\ \\ \frac{2^{6} * 1^3}{7^{3}} = \frac{64}{343} [/tex]
