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

Identify base and exponent: Identify the base and the exponent in (4xy^(2))^(4). In (4xy^(2))^(4), the base is 4xy^(2) and the exponent is 4.Apply power of power rule: Apply the power of a power rule. The power of a power rule states that (a^(m))^n = a^(m*n). Therefore, we can distribute the exponent of 4 to each factor inside the parentheses. (4xy^(2))^(4) = 4^(4) * (x^(1))^4 * (y^(2))^4Simplify each term: Simplify each term. Now we will simplify each term separately. 4^(4) = 4 * 4 * 4 * 4 = 256 (x^(1))^4 = x^(1*4) = x^(4) (y^(2))^4 = y^(2*4) = y^(8)Combine simplified terms: Combine the simplified terms. Now we combine the simplified terms to get the final answer. (4xy^(2))^(4) = 256x^(4)y^(8)

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

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Algebra 2

Evaluate rational exponents

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Q. Fully simplify.

\newline

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

\newline

Answer:

Identify base and exponent: Identify the base and the exponent in 4xy^{2})^{4}\. In \$4xy^{2})^{4}\, the base is \$4xy^{2} and the exponent is ${4}$ .
Apply power of power rule: Apply the power of a power rule. $\newline$ The power of a power rule states that $(a^{m})^{n} = a^{m*n}$ . Therefore, we can distribute the exponent of $4$ to each factor inside the parentheses. $\newline$ $(4xy^{2})^{4} = 4^{4} \times (x^{1})^{4} \times (y^{2})^{4}$
Simplify each term: Simplify each term. $\newline$ Now we will simplify each term separately. $\newline$ $4^{4} = 4 \times 4 \times 4 \times 4 = 256$ $\newline$ $(x^{1})^{4} = x^{1\times4} = x^{4}$ $\newline$ $(y^{2})^{4} = y^{2\times4} = y^{8}$
Combine simplified terms: Combine the simplified terms. $\newline$ Now we combine the simplified terms to get the final answer. $\newline$ $(4xy^{2})^{4} = 256x^{4}y^{8}$