The expression \( \left(x^{2}\right)^{-2}\left(x^{3}\right)^{2} \) is equivalent to \( x^{n} \) What is the value of \( n \) ? A. 2 B. 10 C. 1 D. 9

To simplify the expression \( \left(x^{2}\right)^{-2}\left(x^{3}\right)^{2} \), we can use the power of a power property of exponents, which tells us that \( (a^m)^n = a^{m \cdot n} \). 1. For \( \left(x^{2}\right)^{-2} \): \[ \left(x^{2}\right)^{-2} = x^{2 \cdot (-2)} = x^{-4} \] 2. For \( \left(x^{3}\right)^{2} \): \[ \left(x^{3}\right)^{2} = x^{3 \cdot 2} = x^{6} \] Now we multiply the results: \[ x^{-4} \cdot x^{6} = x^{-4 + 6} = x^{2} \] Thus, the expression simplifies to \( x^{2} \), which means \( n = 2 \). The value of \( n \) is **A. 2**.