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Simplify (6x−2)2(0.5x)4
. Show your work. And d not use any exponents.
To simplify the expression (6x-2)^2 (0.5x)^4, we apply the power of a product rule, which states that (ab)^c = a^c * b^c.
We start by expanding the squares:
(6x-2)^2 = (6x-2)(6x-2) = 36x^2 - 12x - 12x + 4 = 36x^2 - 24x + 4
(0.5x)^4 = (0.5^4)(x^4) = (0.0625)(x^4) = 0.0625x^4
Now, we simplify the expression by multiplying the two terms:
(6x-2)^2 (0.5x)^4 = (36x^2 - 24x + 4)(0.0625x^4)
Using the distributive property, we multiply each term in the first expression by each term in the second expression:
= (36x^2 * 0.0625x^4) + (-24x * 0.0625x^4) + (4 * 0.0625x^4)
= 2.25x^6 - 1.5x^5 + 0.25x^4
Therefore, the simplified expression is 2.25x^6 - 1.5x^5 + 0.25x^4.