Certainly! Let's solve the problem step-by-step for each pair and identify the bigger number in each case.
### Part (a) [tex]$2^5$[/tex] and [tex]$5^2$[/tex]
1. Calculate [tex]$2^5$[/tex]:
[tex]\[
2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32
\][/tex]
2. Calculate [tex]$5^2$[/tex]:
[tex]\[
5^2 = 5 \times 5 = 25
\][/tex]
3. Compare the results:
[tex]\[
32 \quad \text{and} \quad 25
\][/tex]
Clearly, [tex]$32$[/tex] is greater than [tex]$25$[/tex].
Therefore, the bigger number between [tex]\(2^5\)[/tex] and [tex]\(5^2\)[/tex] is [tex]\(32\)[/tex].
### Part (b) [tex]$3^4$[/tex] and [tex]$4^3$[/tex]
1. Calculate [tex]$3^4$[/tex]:
[tex]\[
3^4 = 3 \times 3 \times 3 \times 3 = 81
\][/tex]
2. Calculate [tex]$4^3$[/tex]:
[tex]\[
4^3 = 4 \times 4 \times 4 = 64
\][/tex]
3. Compare the results:
[tex]\[
81 \quad \text{and} \quad 64
\][/tex]
Clearly, [tex]$81$[/tex] is greater than [tex]$64$[/tex].
Therefore, the bigger number between [tex]\(3^4\)[/tex] and [tex]\(4^3\)[/tex] is [tex]\(81\)[/tex].
### Summary of Results:
- For [tex]\(2^5\)[/tex] and [tex]\(5^2\)[/tex], the bigger number is [tex]\(32\)[/tex].
- For [tex]\(3^4\)[/tex] and [tex]\(4^3\)[/tex], the bigger number is [tex]\(81\)[/tex].
Thus, the bigger numbers in each pair are [tex]\(32\)[/tex] and [tex]\(81\)[/tex], respectively.
