Question:- Find
[tex]\left(\frac{5}{12}\right)^{4}\left(\frac{12}{15}\right)^{3}[/tex]
Answer:-
[tex]\left(\frac{5}{12}\right)^{4}\left(\frac{12}{15}\right)^{3}[/tex]
Taking power inside the bracket
[tex] \frac{5^{4} }{ {12}^{4} } \times \frac{ {12}^{3} }{ {15}^{3} } [/tex]
[tex] \frac{ {5}^{4} }{ {12}^{4 - 3} } \times \frac{1}{ {(5 \times 3)}^{3} } \\ \frac{ {5}^{4} }{12} \times \frac{1}{ {5}^{ 3 } \times {3}^{3} } \\ \frac{ {5}^{4 - 3} }{12 \times {3}^{3} } \\ \frac{5}{4 \times 3 \times {3}^{3} } \\ \frac{5}{4 \times {3}^{4} } = \frac{5}{4\times81 } \\ Answer-> \frac{5}{324} [/tex]
[tex]Power\:Form-> \frac{ 5 }{12 \times {3}^{3} } [/tex]
