Simplify ( square root of 64)( fourth root of 128)^3

Math
(64)(1284)3
Rewrite 64 as 82.
82(1284)3
Pull terms out from under the radical, assuming positive real numbers.
8(1284)3
Rewrite 128 as 24⋅8.
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Factor 16 out of 128.
816(8)43
Rewrite 16 as 24.
824⋅843
824⋅843
Pull terms out from under the radical.
8(284)3
Simplify the expression.
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Apply the product rule to 284.
8(23843)
Raise 2 to the power of 3.
8(8843)
8(8843)
Rewrite 843 as (83)14.
8(8834)
Raise 8 to the power of 3.
8(85124)
Rewrite 512 as 44⋅2.
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Factor 256 out of 512.
8(8256(2)4)
Rewrite 256 as 44.
8(844⋅24)
8(844⋅24)
Pull terms out from under the radical.
8(8(424))
Multiply.
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Multiply 4 by 8.
8(3224)
Multiply 32 by 8.
25624
25624
The result can be shown in multiple forms.
Exact Form:
25624
Decimal Form:
304.43702144…
Simplify ( square root of 64)( fourth root of 128)^3

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