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\( x^{36} \)
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To simplify \( \left(x^{4}\right)^{9} \), you'll want to apply the power of a power rule in exponents, which states that \( (a^{m})^{n} = a^{m \cdot n} \). Here, you multiply the exponents: \( 4 \cdot 9 = 36 \). So, we get: \[ \left(x^{4}\right)^{9} = x^{36} \] And there you have it! Simple and sleek: \( x^{36} \)!
