Question

Bracket minus 3 by 8 ki power minus 3 (9 by 4 power minus 3 solve this question

Answer 1

Answer:

$(\frac{32}{27} ) {}^{3}$

Step-by-step explanation:

$( \frac{ { - 3}^{} }{8} ) {}^{ - 3} ( \frac{9}{4} ) {}^{ - 3}$

$(\frac{x}{y }) {}^{ - a} = (\frac{y}{x} ) {}^{a } = \frac{y {}^{a} }{x {}^{a} }$

By above formula

$( \frac{8 {}^{3} }{ { - 3}^{3} } )( \frac{ {4}^{3} }{ {9}^{3} } )$

$\frac{2 {}^{(3 {})^{3} \times 2 {}^{(2)}{}^{3} } }{ - 3 {}^{3} \times ( - 3) {}^{(2)} 3 }$

Therefore - 3 power 2 is 9 and 2 power 3 is 8 and 2 power 2 is 4 so we write it like shown above

$(a {}^{m}) {}^{ n} = a {}^{mn \:} and \: a {}^{m \:} \times a {}^{n \:} \: = {a}^{m + n}$

By applying above identities

$\frac{2 {}^{3 \times 3 + 2 \times 3} }{( - 3) {}^{3 + 2 \times 3} }$

$\frac{2 {}^{15} }{ - 3 {}^{9} } = ( \frac{2 {}^{5} }{3 {}^{3} } ) {}^{3}$

$( \frac{32}{27} ) {}^{3}$

$\frac{32768}{19683}$

$1.66476...........$