Fully simplify. (-3x^(5)y^(2))^(4) Answer:

Identify base and exponent: Identify the base and the exponent in (-3x^(5)y^(2))^(4). In (-3x^(5)y^(2))^(4), the base is (-3x^(5)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^(5)y^(2))^4 = (-3)^4 * (x^5)^4 * (y^2)^4Calculate each part: Calculate each part separately. First, calculate (-3)^4: (-3)^4 = (-3) * (-3) * (-3) * (-3) = 81Calculate (-3)^4: Calculate (x^5)^4: (x^5)^4 = x^(5*4) = x^20Calculate (x^5)^4: Calculate (y^2)^4: (y^2)^4 = y^(2*4) = y^8Calculate (y^2)^4: Combine the results from steps 3, 4, and 5. 81 * x^20 * y^8Combine results: Write the final simplified expression. The fully simplified form is 81x^20y^8.

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Fully simplify.

(-3x^(5)y^(2))^(4)
Answer:

Fully simplify. $\newline$ $\left(-3 x^{5} y^{2}\right)^{4}$ $\newline$ Answer:

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Algebra 2

Evaluate rational exponents

Full solution

Q. Fully simplify.

\newline

\left(-3 x^{5} y^{2}\right)^{4}

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Answer:

Identify base and exponent: Identify the base and the exponent in $(-3x^{5}y^{2})^{4}$ . $\newline$ In $(-3x^{5}y^{2})^{4}$ , the base is $(-3x^{5}y^{2})$ 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. $(-3x^{5}y^{2})^4 = (-3)^4 * (x^5)^4 * (y^2)^4$
Calculate each part: Calculate each part separately. $\newline$ First, calculate $(-3)^4$ : $\newline$ $(-3)^4 = (-3) \times (-3) \times (-3) \times (-3) = 81$
Calculate $(-3)^4$ : Calculate $(x^5)^4$ : $\newline$ $(x^5)^4 = x^{(5*4)} = x^{20}$
Calculate $(x^5)^4$ : Calculate $(y^2)^4$ : $(y^2)^4 = y^{(2*4)} = y^8$
Calculate $(y^2)^4$ : Combine the results from steps $3$ , $4$ , and $5$ . $\newline$ $81 \times x^{20} \times y^8$
Combine results: Write the final simplified expression. $\newline$ The fully simplified form is $81x^{20}y^{8}$ .