Fully simplify. (-3x^(2)y^(2))^(4) Answer:

Identify base and exponent: Identify the base and the exponent in (-3x^(2)y^(2))^(4). In (-3x^(2)y^(2))^(4), the base is -3x^(2)y^(2) and the exponent is 4.Apply power of product rule: Apply the power of a product rule, which states that (ab)^n = a^n * b^n, to the base. (-3x^(2)y^(2))^(4) = (-3)^4 * (x^(2))^4 * (y^(2))^4Calculate each part: Calculate each part separately. (-3)^4 = 81 because (-3) * (-3) * (-3) * (-3) = 81 (x^(2))^4 = x^(2*4) = x^8 because when you raise a power to a power, you multiply the exponents. (y^(2))^4 = y^(2*4) = y^8 for the same reason as x.Multiply results: Multiply the results together. 81 * x^8 * y^8Write final expression: Write the final simplified expression. The simplified form is 81x^8y^8.

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Fully simplify.

(-3x^(2)y^(2))^(4)
Answer:

Fully simplify. $\newline$ $\left(-3 x^{2} y^{2}\right)^{4}$ $\newline$ Answer:

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Algebra 2

Evaluate rational exponents

Full solution

Q. Fully simplify.

\newline

\left(-3 x^{2} y^{2}\right)^{4}

\newline

Answer:

Identify base and exponent: Identify the base and the exponent in $(-3x^{2}y^{2})^{4}$ . $\newline$ In $(-3x^{2}y^{2})^{4}$ , the base is $-3x^{2}y^{2}$ and the exponent is $4$ .
Apply power of product rule: Apply the power of a product rule, which states that $(ab)^n = a^n * b^n$ , to the base. $(-3x^{2}y^{2})^{4} = (-3)^{4} * (x^{2})^{4} * (y^{2})^{4}$
Calculate each part: Calculate each part separately. $\newline$ $(-3)^4 = 81$ because $(-3) \times (-3) \times (-3) \times (-3) = 81$ $\newline$ $(x^{(2)})^4 = x^{(2\times4)} = x^8$ because when you raise a power to a power, you multiply the exponents. $\newline$ $(y^{(2)})^4 = y^{(2\times4)} = y^8$ for the same reason as $x$ .
Multiply results: Multiply the results together. $81 \times x^8 \times y^8$
Write final expression: Write the final simplified expression. $\newline$ The simplified form is $81x^8y^8$ .