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\left(\left(-2\right)^{2}\right)^{5}
Use the rules of exponents to simplify the expression.
\left(-2\right)^{2\times 5}
To raise a power to another power, multiply the exponents.
\left(-2\right)^{10}
Multiply 2 times 5.
1024
Raise -2 to the power 10.