Question
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Tutor-Verified Answer
Answer
\[
\frac{9j^2}{16k^4}
\]
Solution
1. Partimos de la expresión original:
\[
\left(\frac{3j}{4k^2}\right)^2
\]
2. Aplicamos la propiedad de la potencia a la fracción, donde el cuadrado se aplica tanto al numerador como al denominador:
\[
\left(\frac{3j}{4k^2}\right)^2 = \frac{(3j)^2}{(4k^2)^2}
\]
3. Elevamos al cuadrado el numerador:
\[
(3j)^2 = 3^2 \cdot j^2 = 9j^2
\]
4. Elevamos al cuadrado el denominador:
\[
(4k^2)^2 = 4^2 \cdot (k^2)^2 = 16k^4
\]
5. Escribimos la expresión simplificada:
\[
\frac{9j^2}{16k^4}
\]
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Simplify this solution Bonus Knowledge
To simplify \( \left(\frac{3 j}{4 k^{2}}\right)^{2} \), we start by squaring both the numerator and the denominator. The numerator becomes \( (3j)^{2} = 9j^{2} \). The denominator becomes \( (4k^{2})^{2} = 16k^{4} \). Putting it all together, we get: \[ \left(\frac{3 j}{4 k^{2}}\right)^{2} = \frac{9 j^{2}}{16 k^{4}}. \] So, the final answer is \( \frac{9 j^{2}}{16 k^{4}} \).
