Answer :
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]
### (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]