Fully simplify. (-2x^(4)y)^(2) Answer:

Identify base and exponent: Identify the base and the exponent in (-2x^(4)y)^(2). In (-2x^(4)y)^(2), the base is (-2x^(4)y) and the exponent is 2.Apply power of product rule: Apply the power of a product rule, which states that (ab)^n = a^n * b^n, to the base and the exponent. (-2x^(4)y)^(2) = (-2)^2 * (x^(4))^2 * y^2Simplify each term: Simplify each term separately. (-2)^2 = 4 because the square of a negative number is positive. (x^(4))^2 = x^(4*2) = x^8 because of the power of a power rule, which states that (a^m)^n = a^(m*n). y^2 remains as it is because there is no exponent to apply to it.Multiply simplified terms: Multiply the simplified terms together to get the final answer. 4 * x^8 * y^2 = 4x^8y^2

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Fully simplify. $\newline$ $\left(-2 x^{4} y\right)^{2}$ $\newline$ Answer:

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Algebra 2

Evaluate rational exponents

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Q. Fully simplify.

\newline

\left(-2 x^{4} y\right)^{2}

\newline

Answer:

Identify base and exponent: Identify the base and the exponent in $(-2x^{4}y)^{2}$ . $\newline$ In $(-2x^{4}y)^{2}$ , the base is $(-2x^{4}y)$ and the exponent is $2$ .
Apply power of product rule: Apply the power of a product rule, which states that $(ab)^n = a^n \times b^n$ , to the base and the exponent. $\newline$ (\(-2x^{ $4$ }y)^{ $2$ } = ( $-2$ )^ $2$ \times (x^{ $4$ })^ $2$ \times y^ $2$
Simplify each term: Simplify each term separately. $\newline$ $(-2)^2 = 4$ because the square of a negative number is positive. $\newline$ $(x^{4})^2 = x^{4*2} = x^8$ because of the power of a power rule, which states that $(a^m)^n = a^{m*n}$ . $\newline$ $y^2$ remains as it is because there is no exponent to apply to it.
Multiply simplified terms: Multiply the simplified terms together to get the final answer. $4 \times x^8 \times y^2 = 4x^8y^2$