The expression
\frac{4x^{2}y^{3} }{2xy^{4}}
2xy
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4x
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3
is equivalent to
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?
Oh, this expression is like a math joke! It's so simple, it's almost clownishly easy to simplify!
Let's break it down step by step.
First, we can cancel out the common factors in the numerator and denominator. We have 4x^2 in the numerator and 2x in the denominator. So, let's cancel out the 2x:
4x^2 / 2x = 2x
Great! We simplified the first part. Now let's look at the second part.
We have y^3 in the numerator and y^4 in the denominator. Since the exponent in the denominator is greater than the exponent in the numerator, we have to subtract them:
y^4 - y^3 = y^(4-3) = y
Wonderful! We simplified the second part.
Now, let's put the two parts together:
2x * y = 2xy
Voila! The expression is equivalent to 2xy. It's like a simple clown trick, isn't it?
To simplify the expression:
\(\frac{4x^{2}y^{3}}{2xy^{4}}\)
Step 1: Divide the coefficients: \(4 ÷ 2 = 2\).
Step 2: Subtract the exponents in the numerator from the exponents in the denominator:
\(x^{2} ÷ x = x^{2-1} = x\)
\(y^{3} ÷ y^{4} = y^{3-4} = y^{-1} = \frac{1}{y}\)
Putting the results together, the expression simplifies to:
\(\frac {2xy}{y}\)
Further simplifying by cancelling out the \(y\) term:
\(2x\)
To simplify the expression
\frac{4x^{2}y^{3}}{2xy^{4}},
we can simplify the numerator and denominator separately.
In the numerator, we have 4x^2y^3. The term 4 and the term x^2 can be simplified, but y^3 cannot be simplified further.
The term 4 can be expressed as 2 * 2, and the term x^2 can be written as x * x. So we can rewrite the numerator as:
2 * 2 * x * x * y^3.
In the denominator, we have 2xy^4. The term 2 and the term x can be simplified, but y^4 cannot be simplified further.
The term 2 can be expressed as 2 * 1, and the term x can be written as x * 1. So we can rewrite the denominator as:
2 * 1 * x * y^4.
Now we can cancel out the common factors between the numerator and denominator, which are 2, x, and y^3. After canceling out these terms, we are left with:
\frac{2xy^3}{y^4}.
Since the exponent of y in the numerator (3) is smaller than the exponent of y in the denominator (4), we can simplify this expression further by subtracting the exponents:
2xy^{3-4} = 2xy^{-1}.
Writing y^{-1} as 1/y, the simplified expression is:
\frac{2x}{y}.
Therefore, the original expression
\frac{4x^{2}y^{3}}{2xy^{4}}
is equivalent to
\frac{2x}{y}.