To determine which expression is equivalent to \( x^5 \cdot x^2 \), we need to follow the rules of exponents. Specifically, when we multiply expressions that have the same base, we add their exponents. Here's the detailed step-by-step solution:
1. The given expression is \( x^5 \cdot x^2 \).
2. According to the properties of exponents, when multiplying two powers with the same base, we add the exponents. Therefore, \( x^m \cdot x^n = x^{m+n} \).
3. In this case, our bases are both \( x \). The exponents are \( 5 \) and \( 2 \).
4. Add the exponents together:
[tex]\[
5 + 2 = 7
\][/tex]
5. Thus, combining the exponents gives us the expression:
[tex]\[
x^{5+2} = x^7
\][/tex]
Hence, the expression equivalent to \( x^5 \cdot x^2 \) is \( x^7 \).
Therefore, the correct answer is:
[tex]\[ \boxed{x^7} \][/tex]
