[tex]\frac{11}{4 x^2 y^3} \div \frac{1}{4}[/tex]
Answer (2)
Rewrite the division as multiplication by the reciprocal: 4 x 2 y 3 11 ÷ 4 1 = 4 x 2 y 3 11 × 1 4 .
Multiply the numerators and denominators: 4 x 2 y 3 × 1 11 × 4 = 4 x 2 y 3 44 .
Simplify the fraction by cancelling the common factor of 4: 4 x 2 y 3 44 = x 2 y 3 11 .
The simplified expression is: x 2 y 3 11 .
Explanation
Understanding the Problem We are asked to simplify the expression 4 x 2 y 3 11 ÷ 4 1 . This involves dividing one rational expression by another. Remember that dividing by a fraction is the same as multiplying by its reciprocal.
Rewriting the Division To simplify the expression, we rewrite the division as multiplication by the reciprocal of the second fraction: 4 x 2 y 3 11 ÷ 4 1 = 4 x 2 y 3 11 × 1 4
Multiplying the Fractions Now, we multiply the numerators and the denominators: 4 x 2 y 3 × 1 11 × 4 = 4 x 2 y 3 44
Simplifying the Fraction Next, we simplify the fraction by cancelling the common factor of 4 in the numerator and the denominator: 4 x 2 y 3 44 = 4 x 2 y 3 4 × 11 = x 2 y 3 11
Final Answer Therefore, the simplified expression is x 2 y 3 11 .
Examples
Understanding how to simplify rational expressions is crucial in various fields, such as physics and engineering, where complex equations often need to be simplified for easier analysis and computation. For example, in electrical engineering, when analyzing circuits, you might encounter complex impedance expressions that need simplification. Similarly, in fluid dynamics, simplifying expressions involving flow rates and pressures can make problem-solving more manageable. This skill is also valuable in computer graphics for optimizing rendering equations.
The expression 4 x 2 y 3 11 ÷ 4 1 simplifies to x 2 y 3 11 . This is done by rewriting the division as multiplication by the reciprocal, multiplying, and simplifying the resulting fraction. The final answer is x 2 y 3 11 .
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