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

Identify Base and Exponent: Identify the base and the exponent in (5x^(2)y^(2))^(3). In (5x^(2)y^(2))^(3), the base is 5x^(2)y^(2) and the exponent is 3.Apply Power Rule: Apply the power of a product rule. The power of a product rule states that (ab)^n = a^n * b^n. Here, we have three factors inside the parentheses: 5, x^2, and y^2. We will raise each factor to the power of 3. (5x^(2)y^(2))^(3) = 5^3 * (x^2)^3 * (y^2)^3Calculate Powers: Calculate the powers. 5^3 = 5 * 5 * 5 = 125 (x^2)^3 = x^(2*3) = x^6 (y^2)^3 = y^(2*3) = y^6Combine Results: Combine the results. Combine the results from Step 3 to get the final simplified expression. 125 * x^6 * y^6

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Fully simplify.

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

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

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Algebra 2

Evaluate rational exponents

Full solution

Q. Fully simplify.

\newline

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

\newline

Answer:

Identify Base and Exponent: Identify the base and the exponent in $(5x^{2}y^{2})^{3}$ . $\newline$ In $(5x^{2}y^{2})^{3}$ , the base is $5x^{2}y^{2}$ and the exponent is $3$ .
Apply Power Rule: Apply the power of a product rule. $\newline$ The power of a product rule states that $(ab)^n = a^n * b^n$ . Here, we have three factors inside the parentheses: $5$ , $x^2$ , and $y^2$ . We will raise each factor to the power of $3$ . $\newline$ $(5x^{2}y^{2})^{3} = 5^3 * (x^2)^3 * (y^2)^3$
Calculate Powers: Calculate the powers. $\newline$ $5^3 = 5 \times 5 \times 5 = 125$ $\newline$ $(x^2)^3 = x^{(2\times3)} = x^6$ $\newline$ $(y^2)^3 = y^{(2\times3)} = y^6$
Combine Results: Combine the results. $\newline$ Combine the results from Step $3$ to get the final simplified expression. $\newline$ $125 \times x^6 \times y^6$