5. Find the reciprocal of each of the following:

(i) [tex]\left(\frac{3}{8}\right)^4[/tex]

(ii) [tex]\left(\frac{-5}{6}\right)^{11}[/tex]

(iii) [tex]6^7[/tex]



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]