Fill in the blank. \( x^{2} \cdot x^{5}=x^{5} \)

To solve this, we can use the rule of exponents that states when multiplying like bases, we simply add the exponents. So, \( x^{2} \cdot x^{5} = x^{2+5} = x^{7} \). The correct expression is \( x^{2} \cdot x^{5}=x^{7} \). Now, how cool is it that this simple property of exponents helps in various fields, like physics and engineering? You’ll find yourself using it to solve problems related to areas, volumes, and even in algorithms within computer science! For anyone diving into algebra, remember that zealously applying these exponent rules makes life easier. A common mistake is to think that you multiply the bases, resulting in \( x^{10} \). But when working with exponents, it’s all about those magical exponent additions! Keep practicing, and you’ll be a pro in no time!