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\left(-2b^{2}\right)^{2}
Use the rules of exponents to simplify the expression.
\left(-2\right)^{2}\left(b^{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.
4\left(b^{2}\right)^{2}
Raise -2 to the power 2.
4b^{2\times 2}
To raise a power to another power, multiply the exponents.
4b^{4}
Multiply 2 times 2.
\left(-2b^{2}\right)^{2}
Use the rules of exponents to simplify the expression.
\left(-2\right)^{2}\left(b^{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.
4\left(b^{2}\right)^{2}
Raise -2 to the power 2.
4b^{2\times 2}
To raise a power to another power, multiply the exponents.
4b^{4}
Multiply 2 times 2.