To solve these types of exponents problems, we need to understand the concept of raising a number to a power.
Let's go step by step:
(i) This part is unclear, please provide full description and/or context for proper solution.
(ii) Here, you need to fill the blank with the appropriate exponent value for the multiplication of fractions. The expression given is:
[tex]\[ \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} \][/tex]
When you multiply a number by itself multiple times, it is represented as raising the number to the power. In this case, the multiplication occurs 5 times.
[tex]\[ \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} = \left( \frac{1}{3} \right)^{5} \][/tex]
So, the box should be filled with \( 5 \).
(iii) This part is as follows:
\begin{tabular}{c}
\hline[tex]$\frac{1}{m^4}=m$[/tex] \\
\hline[tex]$\frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3}=\left(\frac{1}{3}\right)^5$[/tex] \\
[tex]$7\ 0.004115226337448558$[/tex] \\
\hline
\end{tabular}
In the expression above, you have the same multiplication of \(\frac{1}{3}\) five times. Hence, you write this as:
[tex]\[ \left( \frac{1}{3} \right)^5 \][/tex]
Now, calculate the value:
[tex]\[ \left( \frac{1}{3} \right)^5 \approx 0.004115226337448558 \][/tex]
We see that:
[tex]\[ 7\ 0.004115226337448558\][/tex]
So, the accurately detailed solution demonstrates the multiplication process and the correct use of exponents, where value of the box with [tex]\( \left( \frac{1}{3} \right)^5 \approx 0.004115226337448558 \)[/tex].
