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Answer
La expresión simplificada es \( \frac{180y^{2}}{x^{2}} \).
Solution
Calculate or simplify the expression \( \frac{12 \times 5 y^{4} 12}{4 x^{2} y^{2}} \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{12\times 5y^{4}\times 12}{4x^{2}y^{2}}\)
- step1: Multiply the terms:
\(\frac{720y^{4}}{4x^{2}y^{2}}\)
- step2: Reduce the fraction:
\(\frac{180y^{2}}{x^{2}}\)
La expresión simplificada es \( \frac{180y^{2}}{x^{2}} \).
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Simplify this solution Bonus Knowledge
To simplify the expression \( \frac{12 \times 5 y^{4} 12}{4 x^{2} y^{2}} \), first multiply the constants: \( 12 \times 5 \times 12 = 720 \). The expression then becomes \( \frac{720 y^{4}}{4 x^{2} y^{2}} \). Divide the constant terms: \( 720 \div 4 = 180 \). For the \(y\) terms, use the rule of exponents to subtract the exponents: \( y^{4} \div y^{2} = y^{4-2} = y^{2} \). Thus, the simplified expression is \( \frac{180 y^{2}}{x^{2}} \) or \( \frac{180 y^{2}}{x^{2}} \). This can also be written as \( 180 \frac{y^{2}}{x^{2}} \), which shows that \(y^{2}\) is in the numerator and \(x^{2}\) is in the denominator.
