Which is the simplified form of the expression
( (2^{-3})(x^{-3})(y^{2}) )^{2}
( (4^{-2})(x^{4})(y^{6}) )?
1
1/4x^{2}y^{16}
4/x^{2}y^{16}
1/4x^{14}y^{8}
4/x^{14}y^{8}
Simplifying the expression involving exponents and variables
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To simplify the expression ( left( (2^{-3})(x^{-3})(y^{2}) right)^{2} left( (4^{-2})(x^{4})(y^{6}) right) ), we will break it down step-by-step.
1. Simplify ( (2^{-3})(x^{-3})(y^{2}) ):
– When raised to the power of 2:
[
(2^{-3})^2 = 2^{-6}, quad (x^{-3})^2 = x^{-6}, quad (y^{2})^2 = y^{4}
]
– Thus, ( (2^{-3})(x^{-3})(y^{2}) ) becomes:
[
2^{-6} x^{-6} y^{4}
]
2. Combine the simplified expression:
[
(2^{-6} x^{-6} y^{4}) = 2^{-6} x^{-6} y^{4}
]
3. Now simplify ( (4^{-2})(x^{4})(y^{6}) ):
– Note that ( 4 = 2^2 ), so ( 4^{-2} = (2^2)^{-2} = 2^{-4} ):
[
(4^{-2}) = 2^{-4}, quad