Fully simplify. (-2xy^(2))^(2) Answer:

Identify Base and Exponent: Identify the base and the exponent in (-2xy^(2))^(2). In (-2xy^(2))^(2), Base: -2xy^(2) Exponent: 2Apply Power of Power Rule: Apply the power of a power rule. When raising a power to a power, you multiply the exponents. In this case, the base -2xy^(2) is raised to the power of 2, which means we square each factor in the base. ((-2)^2 * (x)^2 * (y^(2))^2)Calculate Each Part: Calculate each part separately. (-2)^2 = 4 (since squaring a negative number gives a positive result) x^2 = x^2 (raising x to the power of 2) (y^(2))^2 = y^(2*2) = y^4 (multiplying the exponents for y)Combine Results: Combine the results. 4 * x^2 * y^4

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Fully simplify. $\newline$ $\left(-2 x y^{2}\right)^{2}$ $\newline$ Answer:

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Algebra 2

Evaluate rational exponents

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Q. Fully simplify.

\newline

\left(-2 x y^{2}\right)^{2}

\newline

Answer:

Identify Base and Exponent: Identify the base and the exponent in $(-2xy^{2})^{2}$ . $\newline$ In $(-2xy^{2})^{2}$ , $\newline$ Base: $-2xy^{2}$ $\newline$ Exponent: $2$
Apply Power of Power Rule: Apply the power of a power rule. $\newline$ When raising a power to a power, you multiply the exponents. In this case, the base $-2xy^{2}$ is raised to the power of $2$ , which means we square each factor in the base. $\newline$ $((-2)^{2} \cdot (x)^{2} \cdot (y^{2})^{2})$
Calculate Each Part: Calculate each part separately. $\newline$ $(-2)^2 = 4$ (since squaring a negative number gives a positive result) $\newline$ $x^2 = x^2$ (raising $x$ to the power of $2$ ) $\newline$ $(y^{(2)})^2 = y^{(2*2)} = y^4$ (multiplying the exponents for $y$ )
Combine Results: Combine the results. $\newline$ $4 \times x^2 \times y^4$