Question

simplify by usinɡ law of exponents (6⁹×6⁴)÷12⁹​

Answer 1

$= > ( {6}^{9} \times {6}^{4} ) \div {12}^{9} \\ \\ = > ( {6}^{9 + 4} ) \div {12}^{9} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \small \tt \{ \because \: \: {a}^{m} \times {a}^{n} = {a}^{m + n} \} \\ \\ = > {6}^{13} \div {12}^{9} \\ \\ = > \frac{ {6}^{13} }{ {12}^{9} } = \frac{ {6}^{13} }{ {(6 \times 2)}^{9} } \\ \\ = > \frac{ {6}^{13} }{ {6}^{9} \times {2}^{9} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \small \tt \{ \because \: \: {(a \times b)}^{n} = {a}^{n} \times {b}^{n} \} \\ \\ = > \frac{ {6}^{(13 - 9)} }{ {2}^{9} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \small \tt \{ \because \: \: \frac{ {a}^{m} }{ {a}^{n} } = {a}^{(m - n)} \} \\ \\ = > \frac{ {6}^{4} }{ {2}^{9} } = \frac{ {(2 \times 3)}^{4} }{ {2}^{9} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \small \tt \{ \because \: \: {(a \times b)}^{n} = {a}^{n} \times {b}^{n} \}\\ \\ = > \frac{ {2}^{4} \times {3}^{4} }{ {2}^{9} } \\ \\ = > {2}^{(4 - 9)} \times {3}^{4} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \small \tt \{ \because \: \: \frac{ {a}^{m} }{ {a}^{n} } = {a}^{(m - n)} \} \\ \\ = > {2}^{( - 5)} \times {3}^{4} \\ \\ = > \frac{ {3}^{4} }{ {2}^{5} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \small \tt \{ \because \: \: {a}^{( - n)} = \frac{1}{ {a}^{n} } \} \\ \\ = > \frac{3 \times 3 \times 3 \times 3}{2 \times 2 \times 2 \times 2 \times 2} \: \: \: \: = \pink{\frac{81}{32} }$