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\left(3x^{2}\right)^{-4}
Use the rules of exponents to simplify the expression.
3^{-4}\left(x^{2}\right)^{-4}
To raise the product of two or more numbers to a power, raise each number to the power and take their product.
\frac{1}{81}\left(x^{2}\right)^{-4}
Raise 3 to the power -4.
\frac{1}{81}x^{2\left(-4\right)}
To raise a power to another power, multiply the exponents.
\frac{1}{81}\times \frac{1}{x^{8}}
Multiply 2 times -4.
\left(3x^{2}\right)^{-4}
Use the rules of exponents to simplify the expression.
3^{-4}\left(x^{2}\right)^{-4}
To raise the product of two or more numbers to a power, raise each number to the power and take their product.
\frac{1}{81}\left(x^{2}\right)^{-4}
Raise 3 to the power -4.
\frac{1}{81}x^{2\left(-4\right)}
To raise a power to another power, multiply the exponents.
\frac{1}{81}\times \frac{1}{x^{8}}
Multiply 2 times -4.