To determine the number of bacteria in the Petri dish, we need to evaluate the expression [tex]\(2^5 \cdot 3^3 \cdot 10^5\)[/tex] step-by-step:
1. First, calculate [tex]\(2^5\)[/tex]:
[tex]\[
2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32
\][/tex]
2. Next, calculate [tex]\(3^3\)[/tex]:
[tex]\[
3^3 = 3 \times 3 \times 3 = 27
\][/tex]
3. Now, evaluate [tex]\(10^5\)[/tex]:
[tex]\[
10^5 = 10 \times 10 \times 10 \times 10 \times 10 = 100000
\][/tex]
4. Multiply the values obtained from the previous steps:
[tex]\[
32 \times 27 \times 100000
\][/tex]
5. First multiply [tex]\(32 \times 27\)[/tex]:
[tex]\[
32 \times 27 = 864
\][/tex]
6. Finally, multiply the result by [tex]\(10^5\)[/tex]:
[tex]\[
864 \times 100000 = 86400000
\][/tex]
So, the number of bacteria in the Petri dish is [tex]\(86,400,000\)[/tex] bacteria.
