Question

if p/q=(2/3)^2*(1/3)^-4 find the value of (p/q) ^-2

Answer 1

the value of (p/q)^-2 = (1/6)^4

Answer 2

Step-by-step explanation:

It is given that,

$\dfrac{p}{q}=(\dfrac{2}{3})^2\times (\dfrac{1}{3})^{-4}$

We know that,

$(\dfrac{1}{a})^{-x}=a^x$

So,

$\dfrac{p}{q}=(\dfrac{2}{3})^2\times 3^4\\\\\dfrac{p}{q}=6^2$

We need to find the value of $(\dfrac{p}{q})^{-2}$,

So,

$(\dfrac{p}{q})^{-2}=((6)^2)^2\\\\(\dfrac{p}{q})^{-2}=6^{-4}\\\\(\dfrac{p}{q})^{-2}=(\dfrac{1}{6})^4$

Hence, this is the required solution.

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Simplification

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