Answer:
[tex] {9}^{y} = \frac{ {3}^{5} \times {9}^{6} }{ {27}^{3} } \\ [/tex]
• express in terms of 3:
[tex] {3}^{2y} = \frac{ {3}^{5} \times {3}^{12} }{ {3}^{9} } \\ [/tex]
• from law of indices:
[tex] {a}^{n} \times {a}^{m} = {a}^{(n + m)} \\ \\ \frac{ {a}^{n} }{ {a}^{m} } = {a}^{(n - m)} [/tex]
• therefore, let's apply the laws:
[tex] {3}^{2y} = {3}^{(5 + 12 - 9)} \\ \\ {3}^{2y} = {3}^{8} [/tex]
• from third law of indices:
[tex] \{ {a}^{x} = {a}^{y} \} \equiv \{x = y \}[/tex]
• apply the law:
[tex]2y = 8 \\ y = \frac{8}{2 } \\ \\ { \underline{ \underline{ \: \: y = 4 \: \: }}}[/tex]
