Fully simplify. (-4xy^(2))^(2) Answer:

Identify base and exponent: Identify the base and the exponent in (-4xy^2)^2. In (-4xy^2)^2, Base: -4xy^2 Exponent: 2Apply power of power rule: Apply the power of a power rule which states that (a^m)^n = a^(m*n). Here, we have (-4xy^2)^2 = (-4)^2 * (x)^2 * (y^2)^2.Calculate each term: Calculate each term separately. First, (-4)^2 = 16 because the square of a negative number is positive. Second, (x)^2 = x^2 because any variable to the power of 2 is squared. Third, (y^2)^2 = y^(2*2) = y^4 because the power of a power is multiplied.Combine results: Combine the results from the previous step. 16 * x^2 * y^4 is the simplified form of (-4xy^2)^2.Check for further simplification: Check for any possible further simplification. Since there are no like terms to combine and no further powers to apply, the expression is fully simplified.

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

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Algebra 2

Evaluate rational exponents

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Q. Fully simplify.

\newline

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

\newline

Answer:

Identify base and exponent: Identify the base and the exponent in $(-4xy^2)^2$ . $\newline$ In $(-4xy^2)^2$ , Base: $-4xy^2$ Exponent: $2$
Apply power of power rule: Apply the power of a power rule which states that $a^m$ ^n = a^{m*n}. Here, we have \left(\(-4xy^ $2$ \right)^ $2$ = \left( $-4$ \right)^ $2$ \times \left(x\right)^ $2$ \times \left(y^ $2$ \right)^ $2$ .
Calculate each term: Calculate each term separately. $\newline$ First, $(-4)^2 = 16$ because the square of a negative number is positive. $\newline$ Second, $(x)^2 = x^2$ because any variable to the power of $2$ is squared. $\newline$ Third, $(y^2)^2 = y^{(2*2)} = y^4$ because the power of a power is multiplied.
Combine results: Combine the results from the previous step. $16 * x^2 * y^4$ is the simplified form of $(-4xy^2)^2$ .
Check for further simplification: Check for any possible further simplification. Since there are no like terms to combine and no further powers to apply, the expression is fully simplified.