Certainly! Let's find the reciprocal of each given number step by step.
### (i) Reciprocal of [tex]\(\left(\frac{3}{8}\right)^4\)[/tex]
First, we need to evaluate [tex]\(\left(\frac{3}{8}\right)^4\)[/tex].
Given:
[tex]\[
\left(\frac{3}{8}\right)^4
\][/tex]
We are looking for its reciprocal, which is:
[tex]\[
\frac{1}{\left(\frac{3}{8}\right)^4}
\][/tex]
After computing, we find that the reciprocal is approximately:
[tex]\[
50.5679012345679
\][/tex]
### (ii) Reciprocal of [tex]\(\left(\frac{-5}{6}\right)^{11}\)[/tex]
Let's evaluate [tex]\(\left(\frac{-5}{6}\right)^{11}\)[/tex].
Given:
[tex]\[
\left(\frac{-5}{6}\right)^{11}
\][/tex]
We are looking for its reciprocal, which is:
[tex]\[
\frac{1}{\left(\frac{-5}{6}\right)^{11}}
\][/tex]
After computing, we find that the reciprocal is approximately:
[tex]\[
-7.430083706879997
\][/tex]
### (iii) Reciprocal of [tex]\(6^7\)[/tex]
Next, we compute [tex]\(6^7\)[/tex].
Given:
[tex]\[
6^7
\][/tex]
We need its reciprocal, which is:
[tex]\[
\frac{1}{6^7}
\][/tex]
After computing, we find that the reciprocal is approximately:
[tex]\[
3.5722450845907635 \times 10^{-6}
\][/tex]
In summary, the reciprocals of the given numbers are:
[tex]\[
\begin{aligned}
\text{(i)} & \quad 50.5679012345679 \\
\text{(ii)} & \quad -7.430083706879997 \\
\text{(iii)} & \quad 3.5722450845907635 \times 10^{-6}
\end{aligned}
\][/tex]
