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Simplify (6x ^-2(0.5x)^4 . Show your work.
To simplify (6x^-2(0.5x)^4), we can start by expanding the powers.
First, let's expand (0.5x)^4:
(0.5x)^4 = 0.5^4 * x^4
= 0.0625 * x^4 (since 0.5^4 = 0.0625)
Now let's simplify 6x^-2:
6x^-2 = 6 * (1/x^2)
= 6/x^2
Finally, let's combine the two simplified parts:
(6x^-2(0.5x)^4) = (6/x^2) * (0.0625 * x^4)
= 0.375x^2
Therefore, the simplified form of (6x^-2(0.5x)^4) is 0.375x^2.