# Simplify (-10 root of 32* fourth root of 4)^2

(-3210⋅44)2
Rewrite 32 as 25.
(-2510⋅44)2
Rewrite 2510 as 255.
(-255⋅44)2
Pull terms out from under the radical, assuming real numbers.
(-2⋅44)2
Rewrite 4 as 22.
(-2⋅224)2
Rewrite 224 as 22.
(-2⋅22)2
Pull terms out from under the radical, assuming positive real numbers.
(-2⋅2)2
Multiply -22.
Raise 2 to the power of 1.
(-(212))2
Raise 2 to the power of 1.
(-(2121))2
Use the power rule aman=am+n to combine exponents.
(-21+1)2
(-22)2
(-22)2
Rewrite 22 as 2.
Rewrite 2 as 212.
(-(212)2)2
Apply the power rule and multiply exponents, (am)n=amn.
(-212⋅2)2
Combine 12 and 2.
(-222)2
Cancel the common factor of 2.
Cancel the common factor.
(-222)2
Divide 1 by 1.
(-21)2
(-21)2
Evaluate the exponent.
(-1⋅2)2
(-1⋅2)2
Simplify the expression.
Multiply -1 by 2.
(-2)2
Raise -2 to the power of 2.
4
4
Simplify (-10 root of 32* fourth root of 4)^2

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