Question

Find $ \left(\frac{5}{12}\right)^{4}\left(\frac{12}{15}\right)^{3} $.

If thats to hard to read its (5/12)^4 (12/15)^3

Answer 1

Question:- Find

`\left((5)/(12)\right)^(4)\left((12)/(15)\right)^(3)`

Answer:-

`\left((5)/(12)\right)^(4)\left((12)/(15)\right)^(3)`

Taking power inside the bracket

`\frac{5^(4) }{ {12}^(4) } * \frac{ {12}^(3) }{ {15}^(3) }`

`\frac{ {5}^(4) }{ {12}^(4 - 3) } * \frac{1}{ {(5 * 3)}^(3) } \\ \frac{ {5}^(4) }{12} * \frac{1}{ {5}^( 3 ) * {3}^(3) } \\ \frac{ {5}^(4 - 3) }{12 * {3}^(3) } \\ \frac{5}{4 * 3 * {3}^(3) } \\ \frac{5}{4 * {3}^(4) } = (5)/(4*81 ) \\ Answer-> (5)/(324)`

`Power\:Form-> \frac{ 5 }{12 * {3}^(3) }`