To simplify the expression \((6x^3y)(2xy^2)(6x^3y)(2xy^2)\), we can follow these steps:
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Multiply the constants:
First, we multiply the numerical coefficients: \[ 6 \times 2 \times 6 \times 2 = 24 \times 12 = 288. \]
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Multiply the variables:
Next, we multiply the variables, keeping track of the exponents for \(x\) and \(y\).
The expression can be arranged as: \[ (x^3)(x^1)(x^3)(x^1) \text{ for } x \] and \[ (y^1)(y^2)(y^1)(y^2) \text{ for } y. \]
Now, we can apply the exponent rules:
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For \(x\): \[ x^{3+1+3+1} = x^{8}. \]
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For \(y\): \[ y^{1+2+1+2} = y^{6}. \]
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Combine everything:
Now, we combine the constant and variables: \[ 288x^8y^6. \]
Thus, the simplified expression is: \[ \boxed{288x^8y^6}. \]
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