Let's solve the expression [tex]\( 3^2 \cdot 3^5 \)[/tex] step by step:
1. Understanding the Base and Exponents: - We have the same base for both terms, which is 3. - The exponents are [tex]\( 2 \)[/tex] and [tex]\( 5 \)[/tex] respectively.
2. Applying the Properties of Exponents: - According to the properties of exponents, when you multiply two terms with the same base, you add the exponents: [tex]\[
a^m \cdot a^n = a^{m+n}
\][/tex]
3. Combining the Exponents: - Here, the base [tex]\( a \)[/tex] is [tex]\( 3 \)[/tex]. - The exponents [tex]\( m \)[/tex] and [tex]\( n \)[/tex] are [tex]\( 2 \)[/tex] and [tex]\( 5 \)[/tex] respectively. - So, [tex]\[
3^2 \cdot 3^5 = 3^{2+5}
\][/tex]
4. Simplifying the Expression: - Add the exponents: [tex]\[
3^{2+5} = 3^7
\][/tex]
Thus, the expression [tex]\( 3^2 \cdot 3^5 \)[/tex] is equivalent to [tex]\( 3^7 \)[/tex].
Therefore, the correct answer is: [tex]\[
\boxed{3^7}
\][/tex]
