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\left(-4x^{2}\right)^{2}
Use the rules of exponents to simplify the expression.
\left(-4\right)^{2}\left(x^{2}\right)^{2}
To raise the product of two or more numbers to a power, raise each number to the power and take their product.
16\left(x^{2}\right)^{2}
Raise -4 to the power 2.
16x^{2\times 2}
To raise a power to another power, multiply the exponents.
16x^{4}
Multiply 2 times 2.
\left(-4x^{2}\right)^{2}
Use the rules of exponents to simplify the expression.
\left(-4\right)^{2}\left(x^{2}\right)^{2}
To raise the product of two or more numbers to a power, raise each number to the power and take their product.
16\left(x^{2}\right)^{2}
Raise -4 to the power 2.
16x^{2\times 2}
To raise a power to another power, multiply the exponents.
16x^{4}
Multiply 2 times 2.