Question

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fully simplify.

(x^{2}(3y^{3}))

answer attempt 1 out of 2

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Explanation:

Step1: Apply exponent rule to \((3y^3)\)

Using the rule \((ab)^n = a^n b^n\), we have \((3y^3)=3^1\times(y^3)^1 = 3y^3\) (since \(3 = 3^1\) and \((y^3)^1=y^3\) by \(a^1 = a\)).

Step2: Multiply by \(x^2\)

Now, multiply \(x^2\) with \(3y^3\). When multiplying monomials, we multiply the coefficients and the variables separately. The coefficient here is \(1\) (for \(x^2\)) and \(3\) (for \(3y^3\)), so \(1\times3 = 3\). For the variables, we have \(x^2\) and \(y^3\), so combining them we get \(x^2\times3y^3=3x^2y^3\).

Answer:

\(3x^2y^3\)