Fully simplify. (-6x^(2)y^(5))^(2) Answer:

Identify base and exponent: Identify the base and the exponent in (-6x^(2)y^(5))^(2). In (-6x^(2)y^(5))^(2), the base is -6x^(2)y^(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 -6x^(2)y^(5). (-6x^(2)y^(5))^(2) = (-6)^2 * (x^(2))^2 * (y^(5))^2Calculate each part separately: Calculate each part separately. (-6)^2 = 36 because the square of a negative number is positive. (x^(2))^2 = x^(2*2) = x^(4) because of the power of a power rule, which states that (a^m)^n = a^(m*n). (y^(5))^2 = y^(5*2) = y^(10) for the same reason.Combine results: Combine the results from Step 3. 36 * x^(4) * y^(10)Write final simplified expression: Write the final simplified expression. The simplified form is 36x^(4)y^(10).

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Fully simplify.

(-6x^(2)y^(5))^(2)
Answer:

Fully simplify. $\newline$ $\left(-6 x^{2} y^{5}\right)^{2}$ $\newline$ Answer:

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Algebra 2

Evaluate rational exponents

Full solution

Q. Fully simplify.

\newline

\left(-6 x^{2} y^{5}\right)^{2}

\newline

Answer:

Identify base and exponent: Identify the base and the exponent in $(-6x^{2}y^{5})^{2}$ . $\newline$ In $(-6x^{2}y^{5})^{2}$ , the base is $-6x^{2}y^{5}$ 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 $-6x^{2}y^{5}$ . $(-6x^{2}y^{5})^{2} = (-6)^{2} \times (x^{2})^{2} \times (y^{5})^{2}$
Calculate each part separately: Calculate each part separately. $\newline$ $(-6)^2 = 36$ because the square of a negative number is positive. $\newline$ $(x^{2})^2 = x^{(2*2)} = x^{4}$ because of the power of a power rule, which states that $(a^m)^n = a^{(m*n)}$ . $\newline$ $(y^{5})^2 = y^{(5*2)} = y^{10}$ for the same reason.
Combine results: Combine the results from Step $3$ . $36 \times x^{4} \times y^{10}$
Write final simplified expression: Write the final simplified expression. $\newline$ The simplified form is $36x^{4}y^{10}$ .