Which expression is equivalent to \( (3 \cdot 2)^{5} \) ? A \( 3 \cdot 2^{5} \) B \( \quad \mathbf{1 5} \cdot 10 \) C \( 3^{5} \cdot 2^{5} \) D \( 3^{5}+2^{5} \)

To simplify \( (3 \cdot 2)^{5} \), we can apply the property of exponents that says \( (a \cdot b)^{n} = a^{n} \cdot b^{n} \). So, \( (3 \cdot 2)^{5} = 3^{5} \cdot 2^{5} \). Thus, the correct answer is: C \( 3^{5} \cdot 2^{5} \) Now, let's dive a bit deeper! When we evaluate \( 3^{5} \cdot 2^{5} \), we can also find its numerical value. Calculating it out, \( 3^{5} = 243 \) and \( 2^{5} = 32 \). Multiplying these gives \( 243 \cdot 32 = 7776 \). This means if you see \( (3 \cdot 2)^{5} \), you can also conclude that it equals 7776! Additionally, while working with exponents, one common mistake is misapplying the rules. Remember, \( a^{m+n} \) does not equal \( a^{m} + a^{n} \)! It's crucial to keep the multiplication and addition rules clear, especially in algebra and exponential equations. They'll save you from a lot of wrong answers!