Fully simplify. (-5x^(5)y^(3))^(2) Answer:

Identify base and exponent: Identify the base and the exponent in (-5x^(5)y^(3))^(2). In (-5x^(5)y^(3))^(2), the base is (-5x^(5)y^(3)) 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^(5)y^(3))^(2) = (-5)^2 * (x^(5))^2 * (y^(3))^2Calculate each part: Calculate each part separately. (-5)^2 = 25 because the square of a negative number is positive. (x^(5))^2 = x^(5*2) = x^(10) because of the power of a power rule, which states that (a^m)^n = a^(m*n). (y^(3))^2 = y^(3*2) = y^(6) for the same reason.Combine results: Combine the results from Step 3. 25 * x^(10) * y^(6)Final simplified form: Since there are no like terms to combine, this is the simplified form.

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Fully simplify.

(-5x^(5)y^(3))^(2)
Answer:

Fully simplify. $\newline$ $\left(-5 x^{5} y^{3}\right)^{2}$ $\newline$ Answer:

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Algebra 2

Evaluate rational exponents

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Q. Fully simplify.

\newline

\left(-5 x^{5} y^{3}\right)^{2}

\newline

Answer:

Identify base and exponent: Identify the base and the exponent in $(-5x^{5}y^{3})^{2}$ . $\newline$ In $(-5x^{5}y^{3})^{2}$ , the base is $(-5x^{5}y^{3})$ 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^{ $5$ }y^{ $3$ })^{ $2$ } = ( $-5$ )^ $2$ \times (x^{ $5$ })^ $2$ \times (y^{ $3$ })^ $2$
Calculate each part: Calculate each part separately. $\newline$ $(-5)^2 = 25$ because the square of a negative number is positive. $\newline$ $(x^{5})^2 = x^{5*2} = x^{10}$ because of the power of a power rule, which states that $(a^m)^n = a^{m*n}$ . $\newline$ $(y^{3})^2 = y^{3*2} = y^{6}$ for the same reason.
Combine results: Combine the results from Step $3$ . $25 \times x^{10} \times y^{6}$
Final simplified form: Since there are no like terms to combine, this is the simplified form.