Question

Simplify: 2^-5 X 3^-5 x 125÷
5^-4 X 6^-5​

Answer 1

Answer:

$({2}^{ - 5} \times {3}^{ - 5} \times 125) \div ( {5}^{ - 4} \times {6}^{ - 5} ) \\ = \frac{ {2}^{ - 5} \times {3}^{ - 5} \times 125 }{ {5}^{ - 4} \times {6}^{ - 5} } \\ = \frac{ {5}^{4} \times {6}^{5} \times 125 }{ {2}^{5} \times {3}^{5} } \\ = \frac{ {5}^{4} \times {(2 \times 3)}^{5} \times {5}^{3} }{ {2}^{5} \times {3}^{5} } \\ = \frac{ {5}^{4} \times {2}^{5} \times {3}^{5} \times {5}^{3} }{ {2}^{5} \times {3}^{5} } \\ = \frac{ {(5)}^{4 + 3} \times {2}^{5} \times {3}^{5} }{ {2}^{5} \times {3}^{5}} \\ = \frac{ {5}^{7} \times {2}^{5} \times {3}^{5}}{ {2}^{5} \times {3}^{5}} \\ = {5}^{7} \times {(2)}^{5 - 5} \times {(3)}^{5 - 5} \\ = {5}^{7} \times {2}^{0} \times {3}^{0} \\ = {5}^{7} \times 1 \times 1 \\ \large{ \boxed{ = \color{crimson} {5}^{7} }} \\ \\ \underline{ \underline{ \large Note}} : \\ ◈ \: \: \color{crimson} {(a \times b)}^{m} = {a}^{m} \times {b}^{m} \\ ◈ \: \: \color{crimson} {a}^{m} \times {a}^{n} = {(a)}^{m + n} \\ ◈ \: \: \color{crimson} \frac{ {a}^{m} }{ {a}^{n} } = {(a)}^{m - n} \\ ◈ \: \: \color{crimson} {a}^{0} = 1$