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Answer :
Let's simplify the expression [tex]\(\frac{15 x^9 y^4}{5 x^4 y^2}\)[/tex] step-by-step.
1. Simplify the Coefficient:
- Look at the numbers in the numerator and the denominator. We have 15 in the numerator and 5 in the denominator.
- Divide 15 by 5, which gives us 3.
2. Simplify the [tex]\(x\)[/tex]-terms:
- We have [tex]\(x^9\)[/tex] in the numerator and [tex]\(x^4\)[/tex] in the denominator.
- Subtract the exponent in the denominator from the exponent in the numerator: [tex]\(9 - 4 = 5\)[/tex].
- So, the [tex]\(x\)[/tex]-term simplifies to [tex]\(x^5\)[/tex].
3. Simplify the [tex]\(y\)[/tex]-terms:
- Similarly, we have [tex]\(y^4\)[/tex] in the numerator and [tex]\(y^2\)[/tex] in the denominator.
- Subtract the exponent in the denominator from the exponent in the numerator: [tex]\(4 - 2 = 2\)[/tex].
- So, the [tex]\(y\)[/tex]-term simplifies to [tex]\(y^2\)[/tex].
Putting it all together, the simplified expression is [tex]\(3x^5y^2\)[/tex].
Therefore, the correct simplified form is [tex]\(\boxed{3x^5y^2}\)[/tex].
1. Simplify the Coefficient:
- Look at the numbers in the numerator and the denominator. We have 15 in the numerator and 5 in the denominator.
- Divide 15 by 5, which gives us 3.
2. Simplify the [tex]\(x\)[/tex]-terms:
- We have [tex]\(x^9\)[/tex] in the numerator and [tex]\(x^4\)[/tex] in the denominator.
- Subtract the exponent in the denominator from the exponent in the numerator: [tex]\(9 - 4 = 5\)[/tex].
- So, the [tex]\(x\)[/tex]-term simplifies to [tex]\(x^5\)[/tex].
3. Simplify the [tex]\(y\)[/tex]-terms:
- Similarly, we have [tex]\(y^4\)[/tex] in the numerator and [tex]\(y^2\)[/tex] in the denominator.
- Subtract the exponent in the denominator from the exponent in the numerator: [tex]\(4 - 2 = 2\)[/tex].
- So, the [tex]\(y\)[/tex]-term simplifies to [tex]\(y^2\)[/tex].
Putting it all together, the simplified expression is [tex]\(3x^5y^2\)[/tex].
Therefore, the correct simplified form is [tex]\(\boxed{3x^5y^2}\)[/tex].
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