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\left(\left(-10\right)^{2}\right)^{2}
Use the rules of exponents to simplify the expression.
\left(-10\right)^{2\times 2}
To raise a power to another power, multiply the exponents.
\left(-10\right)^{4}
Multiply 2 times 2.
10000
Raise -10 to the power 4.