Question

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

Answer 1

Answer:

Step-by-step explanation:

It is given that,

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

q

p

=(

3

2

)

2

×(

3

)

−4

We know that,

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

a

1

)

−x

=a

x

So,

\begin{gathered}\dfrac{p}{q}=(\dfrac{2}{3})^2\times 3^4\\\\\dfrac{p}{q}=6^2\end{gathered}

q

p

=(

3

2

)

2

×3

4

q

p

=6

2

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

q

p

)

−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}

(

q

p

)

−2

=((6)

2

)

2

(

q

p

)

−2

=6

−4

(

q

p

)

−2

=(

6

1

)

4