Question

plzz Simplyfy this question​

Answer 1

Question :

Simplify $\sf{\bigg(\dfrac{18}{16}\bigg)^{-3/4}}$

Required Solution :

$\\ \implies\sf{\bigg(\dfrac{18}{16}\bigg)^{-3/4}}$

• Cancelling 18 and 16 we get ;

$\\ \implies\sf{\bigg(\dfrac{18}{16}\bigg)^{-3/4}} \\ \\ \\ \implies \sf \bigg( \frac{9}{8} \bigg)^{ - 3 / 4}$

• Using the identity , $\sf{a^{-n}=\dfrac{1}{a^n}}$

$\\ \implies \sf \bigg( \frac{ 8}{9} \bigg)^{ 3/4}$

• Using the identity , $\sf{\bigg(\dfrac{a}{b}\bigg)^{m}=\dfrac{a^m}{b^m}}$

$\\ \implies\sf\bigg(\dfrac{8 {}^{3/4} }{9 {}^{3/4} }\bigg)$

• Writing eight as two to the power 3 [Since 8 is the cube of 2] we get ;

$\\ \sf \implies \sf \bigg( \frac{2 {}^{(3) {}^{3/4} } }{9 {}^{3/4} } \bigg)$

• Using the identity , $\sf {a^{m {}^{(n)} } = a^{mn}}$

$\\ \sf\implies \bigg( \frac{ {2}^{9/4} }{9 {}^{3/4} } \bigg)$

• Writing nine as three to the power two [Since 9 is the square of 3] we get ;

$\\ \implies \sf \bigg( \frac{ {2}^{9/4} }{3 {}^{(2) {}^{3/4} } } \bigg)$

• Using the identity , $\sf {a^{m {}^{(n)} } = a^{mn}}$

$\\ \implies \sf \bigg( \frac{ {2}^{9/4} }{ {3}^{3/2} } \bigg) \\ \\ \\ \implies{\underline{\boxed{\sf{{\bigg(\dfrac{18}{16}\bigg)^{-3/4}} = \sf \bigg( \frac{ {2}^{9/4} }{ {3}^{3/2} } \bigg) }}}}$