Question

simplify [(-3/4)^4 × (-3/4)^-2] ÷ [(3/4)^2]^-2​

Answer 1

$\bigg [\sf{ \bigg(\frac{ - 3}{4} \bigg) ^{4} \times \bigg(\frac{ - 3}{2} \bigg) \bigg] ^{3} }\\ \\ \sf{= \bigg[ {\frac{ - 3}{4}}^{ \big(\frac{(4+2)}{( \frac{3}{4})} \big) ^{2} } \bigg] ^{3} }\\ \\ = \bigg[ \bigg \{ \frac{(\frac{ - 3}{4} )^6}{( \frac{3}{4} ) ^{2} }\bigg \} \bigg]^{3} \\ \\ \sf{we \: know, }\\ \sf{(-x)ⁿ = xⁿ \: when \: n = even \: number }\\ \\ \sf{so , \bigg ( \frac{3}{4} \bigg )^{2} = \bigg ( \frac{-3}{4} \bigg) ^{2} } \\ \\ \sf{use \: this \: here , }\\ \\ = \sf{ \bigg[ \bigg ( \frac{-3}{4} \bigg)^{(6-2)} \bigg]^{3} }\\ \\ = \sf{ \bigg[ \bigg( \frac{3}{4} \bigg) ^{4} \bigg ] ^{3} }\\ \\ \boxed{ \purple{ \bigg( \frac{3}{4}\bigg)^{12}} }$

Answer 2

Answer:

$\begin{gathered} \bigg [\sf{ \bigg(\frac{ - 3}{4} \bigg) ^{4} \times \bigg(\frac{ - 3}{2} \bigg) \bigg] ^{3} }\\ \\ \sf{= \bigg[ {\frac{ - 3}{4}}^{ \big(\frac{(4+2)}{( \frac{3}{4})} \big) ^{2} } \bigg] ^{3} }\\ \\ = \bigg[ \bigg \{ \frac{(\frac{ - 3}{4} )^6}{( \frac{3}{4} ) ^{2} }\bigg \} \bigg]^{3} \\ \\ \sf{we \: know, }\\ \sf{(-x)ⁿ = xⁿ \: when \: n = even \: number }\\ \\ \sf{so , \bigg ( \frac{3}{4} \bigg )^{2} = \bigg ( \frac{-3}{4} \bigg) ^{2} } \\ \\ \sf{use \: this \: here , }\\ \\ = \sf{ \bigg[ \bigg ( \frac{-3}{4} \bigg)^{(6-2)} \bigg]^{3} }\\ \\ = \sf{ \bigg[ \bigg( \frac{3}{4} \bigg) ^{4} \bigg ] ^{3} }\\ \\ \boxed{ \orange{ \bigg( \frac{3}{4}\bigg)^{12}} }\\ \\ \end{gathered} </p><p>$