sqrt((99x^(12))/(25y^(12)))

Split and Simplify: Simplify the square root of a fraction by taking the square root of the numerator and the denominator separately. We have sqrt((99x^(12))/(25y^(12))). The square root of 99x^(12) is sqrt(99) * sqrt(x^(12)), and the square root of 25y^(12) is sqrt(25) * sqrt(y^(12)).Simplify Perfect Squares: Simplify the square roots of the perfect squares and the variables with even exponents. sqrt(99) is not a perfect square, but we can simplify sqrt(x^(12)) to x^(6) because the exponent is even and divisible by 2. Similarly, sqrt(25) simplifies to 5, and sqrt(y^(12)) simplifies to y^(6).Simplify sqrt(99): Simplify sqrt(99). Since 99 is 9 * 11 and 9 is a perfect square, we can write sqrt(99) as sqrt(9) * sqrt(11), which simplifies to 3 * sqrt(11).Combine Simplified Terms: Combine the simplified terms. We now have (3 * sqrt(11) * x^(6)) / (5 * y^(6)). Since x and y are both positive, we can keep the terms as they are without worrying about absolute values.Write Final Expression: Write the final simplified expression. The simplified form of the original expression is (3 * sqrt(11) * x^(6)) / (5 * y^(6)).

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$\sqrt{\frac{99 x^{12}}{25 y^{12}}}$

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\sqrt{\frac{99 x^{12}}{25 y^{12}}}

Split and Simplify: Simplify the square root of a fraction by taking the square root of the numerator and the denominator separately. $\newline$ We have $\sqrt{\frac{99x^{12}}{25y^{12}}}$ . The square root of $99x^{12}$ is $\sqrt{99} \times \sqrt{x^{12}}$ , and the square root of $25y^{12}$ is $\sqrt{25} \times \sqrt{y^{12}}$ .
Simplify Perfect Squares: Simplify the square roots of the perfect squares and the variables with even exponents. $\sqrt{99}$ is not a perfect square, but we can simplify $\sqrt{x^{12}}$ to $x^{6}$ because the exponent is even and divisible by $2$ . Similarly, $\sqrt{25}$ simplifies to $5$ , and $\sqrt{y^{12}}$ simplifies to $y^{6}$ .
Simplify $\sqrt{99}$ : Simplify $\sqrt{99}$ . $\newline$ Since $99$ is $9 \times 11$ and $9$ is a perfect square, we can write $\sqrt{99}$ as $\sqrt{9} \times \sqrt{11}$ , which simplifies to $3 \times \sqrt{11}$ .
Combine Simplified Terms: Combine the simplified terms. $\newline$ We now have $(3 \cdot \sqrt{11} \cdot x^{6}) / (5 \cdot y^{6})$ . Since $x$ and $y$ are both positive, we can keep the terms as they are without worrying about absolute values.
Write Final Expression: Write the final simplified expression. $\newline$ The simplified form of the original expression is $(\frac{3 \cdot \sqrt{11} \cdot x^{6}}{5 \cdot y^{6}})$ .