Question

Simplify:


`\sf \: ((4/7)^5 * (2 / 3)^4 )/((4 / 9) * (4 / 7)^ 3)`

Answer 1

`\qquad \qquad\huge \underline{\boxed{\sf ᴀɴsweʀ}}`

Here's the solution ~

`\qquad \sf  \dashrightarrow \: ((4/7)^5 * (2 / 3)^4 )/((4 / 9) * (4 / 7)^ 3)`

`\qquad \sf  \dashrightarrow \: \frac{ ((4)/(7)) {}^(5) }{ ((4)/(7) ) {}^(3) } * \frac{( (2)/(3))^(4) } { (4)/(9) }`

`\qquad \sf  \dashrightarrow \: \frac{ ((4)/(7)) {}^(5) }{ ((4)/(7) ) {}^(3) } * \frac{( (2)/(3))^(4) } { \frac{ {2}^(2) }{ {3}^(2) } }`

`\qquad \sf  \dashrightarrow \: \frac{ ((4)/(7)) {}^(5) }{ ((4)/(7) ) {}^(3) } * \frac{( (2)/(3))^(4) } {( (2)/(3) ) {}^(2) }`

`\qquad \sf  \dashrightarrow \: ( (4)/(7)) {}^(2) * ( (2)/(3) ) {}^(2)`

`\qquad \sf  \dashrightarrow \: (16)/(49) * (4)/(9)`

`\qquad \sf  \dashrightarrow \: (64)/(441)`