To find the product of [tex]\(5^2 \cdot 5^8\)[/tex] and write the answer in exponential form, we can use the property of exponents that states:
[tex]\[ a^m \cdot a^n = a^{m+n} \][/tex]
Here, the base [tex]\(a\)[/tex] is 5, and we have two exponents: [tex]\(m = 2\)[/tex] and [tex]\(n = 8\)[/tex]. According to the property, we simply add the exponents together.
Step-by-step solution:
1. Identify the base and the exponents:
[tex]\[
\text{Base} = 5, \quad \text{Exponents} = 2 \text{ and } 8
\][/tex]
2. Add the exponents:
[tex]\[
2 + 8 = 10
\][/tex]
3. Write the final expression, using the sum of the exponents:
[tex]\[
5^{2+8} = 5^{10}
\][/tex]
Thus, the product [tex]\(5^2 \cdot 5^8\)[/tex] can be written in exponential form as:
[tex]\[
5^{10}
\][/tex]
So the correct answer is [tex]\(5^{10}\)[/tex], and the exponent of the resulting expression is 10.
