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

Identify base and exponents: Identify the base and the exponents in (-5x^2y^5)^2. In (-5x^2y^5)^2, the base is -5x^2y^5 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 -5x^2y^5 raised to the power of 2. (-5x^2y^5)^2 = (-5)^2 * (x^2)^2 * (y^5)^2Calculate each term: Calculate each term separately. (-5)^2 = 25 because the square of a negative number is positive. (x^2)^2 = x^(2*2) = x^4 because when you raise a power to a power, you multiply the exponents. (y^5)^2 = y^(5*2) = y^10 for the same reason.Combine results: Combine the results from the previous step to get the final simplified expression. 25 * x^4 * y^10Write final expression: Write the final simplified expression as a single term. 25x^4y^10

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Fully simplify.

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

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

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Algebra 2

Evaluate rational exponents

Full solution

Q. Fully simplify.

\newline

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

\newline

Answer:

Identify base and exponents: Identify the base and the exponents in $(-5x^2y^5)^2$ . $\newline$ In $(-5x^2y^5)^2$ , the base is $-5x^2y^5$ 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 $-5x^2y^5$ raised to the power of $2$ . $(-5x^2y^5)^2 = (-5)^2 \times (x^2)^2 \times (y^5)^2$
Calculate each term: Calculate each term separately. $\newline$ $(-5)^2 = 25$ because the square of a negative number is positive. $\newline$ $(x^2)^2 = x^{(2*2)} = x^4$ because when you raise a power to a power, you multiply the exponents. $\newline$ $(y^5)^2 = y^{(5*2)} = y^{10}$ for the same reason.
Combine results: Combine the results from the previous step to get the final simplified expression. $25 * x^4 * y^{10}$
Write final expression: Write the final simplified expression as a single term. $25x^4y^{10}$