Question

if x = (-7/2) power4 ÷(-7/2)power5 × (-7/2)power 0 ×(-7/2)power 2 , find the value of x power-3 .​

Answer 1

ANSWER✔

$\large\underline\bold{GIVEN,}$

$\sf\dashrightarrow x= \left( \left( \dfrac{\dfrac{-7}{2}}{\dfrac{-7}{2}} \right)^5 \times \bigg(\dfrac{-7}{2} \bigg)^0 \times \bigg( \dfrac{-7}{2} \bigg)^2 \right){-3}$

$\large\underline\bold{TO\:FIND,}$

$\sf\dashrightarrow \:THE\:VALUE\:OF\:X$

✯IDENTITY IN USE,

$\large{\boxed{\bf{ \star\:\: a^0=1 \:\: \star}}}$

$\large\underline\bold{SOLUTION,}$

$\sf\therefore x= \left( \left( \dfrac{\dfrac{-7}{2}}{\dfrac{-7}{2}} \right)^5 \times \bigg(\dfrac{-7}{2} \bigg)^0 \times \bigg( \dfrac{-7}{2} \bigg)^2 \right){-3}$

$\sf\implies x= \left( \cancel{\left( \dfrac{\dfrac{-7}{2}}{\dfrac{-7}{2}} \right)}^5 \times 1 \times \bigg( \dfrac{-7}{2} \bigg)^2 \right){-3}$

$\sf\implies \left( 1 \times 1 \times \bigg( \dfrac{49}{4} \bigg) \right)^{-3}$

$\sf\implies\bigg( \dfrac{49}{4} \bigg)^{-3}$

$\sf\implies\bigg( \dfrac{4}{49} \bigg)^3$

$\sf\implies \bigg(\dfrac{4}{49} \times \dfrac{4}{49} \times \dfrac{4}{49} \bigg)$

$\sf\implies \dfrac{4\times 4\times 4 }{ 49 \times 49 \times 49}$

$\sf\implies \dfrac{64}{117649}$

$\large{\boxed{\bf{ \star\:\:x= \dfrac{64}{117649} \:\: \star}}}$

_________________

Answer 2

$\large\underline{\underline{\bold{\pink{\mathfrak{AnSwEr}}}}}$

$\large\underline\bold{GIVEN,}$

$\sf\dashrightarrow x= \left( \left( \dfrac{\dfrac{-7}{2}}{\dfrac{-7}{2}} \right)^5 \times \bigg(\dfrac{-7}{2} \bigg)^0 \times \bigg( \dfrac{-7}{2} \bigg)^2 \right){-3}$

$\large\underline\bold{TO\:FIND,}$

$\sf\dashrightarrow \:THE\:VALUE\:OF\:X$

IDENTITY IN USE,

$\large{\boxed{\bf{ \star\:\: a^0=1 \:\: \star}}}$

$\large\underline\bold{SOLUTION,}$

$\sf\therefore x= \left( \left( \dfrac{\dfrac{-7}{2}}{\dfrac{-7}{2}} \right)^5 \times \bigg(\dfrac{-7}{2} \bigg)^0 \times \bigg( \dfrac{-7}{2} \bigg)^2 \right){-3}$

$\sf\implies x= \left( \cancel{\left( \dfrac{\dfrac{-7}{2}}{\dfrac{-7}{2}} \right)}^5 \times 1 \times \bigg( \dfrac{-7}{2} \bigg)^2 \right){-3}$

$\sf\implies \left( 1 \times 1 \times \bigg( \dfrac{49}{4} \bigg) \right)^{-3}$

$\sf\implies\bigg( \dfrac{49}{4} \bigg)^{-3}$

$\sf\implies\bigg( \dfrac{4}{49} \bigg)^3$

$\sf\implies \bigg(\dfrac{4}{49} \times \dfrac{4}{49} \times \dfrac{4}{49} \bigg)$

$\sf\implies \dfrac{4\times 4\times 4 }{ 49 \times 49 \times 49}$

$\sf\implies \dfrac{64}{117649}$

$\large{\boxed{\bf{ \star\:\:x= \dfrac{64}{117649} \:\: \star}}}$