Fully simplify. (-3xy^(5))^(4) Answer:

Identify base and exponent: Identify the base and the exponent in (-3xy^5)^4. In (-3xy^5)^4, the base is -3xy^5 and the exponent is 4.Apply power rule: Apply the power rule (a*b)^n = a^n * b^n to the base -3xy^5. (-3xy^5)^4 = (-3)^4 * (x)^4 * (y^5)^4Calculate each part: Calculate each part separately. (-3)^4 = 81 because (-3) multiplied by itself 4 times is positive 81. x^4 remains as it is because there is no numerical calculation to perform. (y^5)^4 = y^(5*4) = y^20 because when you raise a power to a power, you multiply the exponents.Combine results: Combine the results from the previous step. 81 * x^4 * y^20Write final expression: Write the final simplified expression. The fully simplified expression is 81x^4y^20.

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Fully simplify. $\newline$ $\left(-3 x y^{5}\right)^{4}$ $\newline$ Answer:

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Algebra 2

Evaluate rational exponents

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Q. Fully simplify.

\newline

\left(-3 x y^{5}\right)^{4}

\newline

Answer:

Identify base and exponent: Identify the base and the exponent in $(-3xy^5)^4$ . $\newline$ In $(-3xy^5)^4$ , the base is $-3xy^5$ and the exponent is $4$ .
Apply power rule: Apply the power rule $(a*b)^n = a^n * b^n$ to the base $-3xy^5$ . $(-3xy^5)^4 = (-3)^4 * (x)^4 * (y^5)^4$
Calculate each part: Calculate each part separately. $\newline$ $(-3)^4 = 81$ because $(-3)$ multiplied by itself $4$ times is positive $81$ . $\newline$ $x^4$ remains as it is because there is no numerical calculation to perform. $\newline$ $(y^5)^4 = y^{(5*4)} = y^{20}$ because when you raise a power to a power, you multiply the exponents.
Combine results: Combine the results from the previous step. $81 * x^4 * y^{20}$
Write final expression: Write the final simplified expression. $\newline$ The fully simplified expression is $81x^4y^{20}$ .