Fully simplify. (-4x^(2)y^(5))^(4) Answer:

Identify base and exponents: Identify the base and the exponents in (-4x^2y^5)^4. In (-4x^2y^5)^4, the base is -4x^2y^5 and the exponent is 4.Apply power rule: Apply the power rule (a*b)^n = a^n * b^n to the expression. (-4x^2y^5)^4 can be written as (-4)^4 * (x^2)^4 * (y^5)^4.Calculate each part: Calculate each part separately. First, (-4)^4 = 256 because a negative number raised to an even power is positive. Second, (x^2)^4 = x^(2*4) = x^8 because of the power of a power rule, which states that (a^m)^n = a^(m*n). Third, (y^5)^4 = y^(5*4) = y^20 for the same reason.Combine results: Combine the results from the previous step. The expression simplifies to 256 * x^8 * y^20.Write final expression: Write the final simplified expression. The fully simplified form of (-4x^2y^5)^4 is 256x^8y^20.

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Fully simplify.

(-4x^(2)y^(5))^(4)
Answer:

Fully simplify. $\newline$ $\left(-4 x^{2} y^{5}\right)^{4}$ $\newline$ Answer:

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Algebra 2

Evaluate rational exponents

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Q. Fully simplify.

\newline

\left(-4 x^{2} y^{5}\right)^{4}

\newline

Answer:

Identify base and exponents: Identify the base and the exponents in $(-4x^2y^5)^4$ . $\newline$ In $(-4x^2y^5)^4$ , the base is $-4x^2y^5$ and the exponent is $4$ .
Apply power rule: Apply the power rule $(a*b)^n = a^n * b^n$ to the expression. $(-4x^2y^5)^4$ can be written as $(-4)^4 * (x^2)^4 * (y^5)^4$ .
Calculate each part: Calculate each part separately. $\newline$ First, $(-4)^4 = 256$ because a negative number raised to an even power is positive. $\newline$ Second, $(x^2)^4 = x^{(2*4)} = x^8$ because of the power of a power rule, which states that $(a^m)^n = a^{(m*n)}$ . $\newline$ Third, $(y^5)^4 = y^{(5*4)} = y^{20}$ for the same reason.
Combine results: Combine the results from the previous step. The expression simplifies to $256 \times x^8 \times y^{20}$ .
Write final expression: Write the final simplified expression. $\newline$ The fully simplified form of $(-4x^2y^5)^4$ is $256x^8y^{20}$ .