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If p/q=(2/3)^2×(1/3)^-4 find the value of (p/q)^-2 |
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Answer» Step-by-step explanation:It is given that,\dfrac{p}{q}=(\dfrac{2}{3})^2\times (\dfrac{1}{3})^{-4} qp =( 32 ) 2 ×( 3 ) −4 We know that,(\dfrac{1}{a})^{-x}=a^x( a1 ) −x =a x So,\begin{gathered}\dfrac{p}{q}=(\dfrac{2}{3})^2\times 3^4\\\\\dfrac{p}{q}=6^2\end{gathered} qp =( 32 ) 2 ×3 4 qp =6 2 We need to find the value of (\dfrac{p}{q})^{-2}( qp ) −2 ,So,\begin{gathered}(\dfrac{p}{q})^{-2}=((6)^2)^2\\\\(\dfrac{p}{q})^{-2}=6^{-4}\\\\(\dfrac{p}{q})^{-2}=(\dfrac{1}{6})^4\end{gathered} ( qp ) −2 =((6) 2 ) 2 ( qp ) −2 =6 −4 ( qp ) −2 =( 61 ) 4 |
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