To simplify the expression \( 162x65 \), we first need to calculate \( 162 \times 65 \).
Calculating \( 162 \times 65 \): \[ 162 \times 65 = 10530 \]
Now, let's simplify the other expressions that were provided:
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\( 12x^1y\sqrt{7xy^2} \)
- This expression cannot be simplified further without specific values for \( x \) and \( y \).
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\( 9xy^2\sqrt{\sqrt{2x5y^3}} \)
- First, simplify the inner square root: \(\sqrt{2x5y^3} = \sqrt{10xy^3}\)
- Therefore, \[ \sqrt{10xy^3} = \sqrt{10}\sqrt{x}\sqrt{y^3} = \sqrt{10}xy\sqrt{y} \]
- Therefore: \[ 9xy^2\sqrt{\sqrt{2x5y^3}} = 9xy^2\sqrt{10}xy\sqrt{y} = 9\sqrt{10}xy^3 \]
-
\( \frac{9x^3y^2}{2y} \)
- This can be simplified by canceling \( y \): \[ \frac{9x^3y^2}{2y} = \frac{9x^3y}{2} \]
Lastly, we can compare the simplified forms to see which one matches the original number \( 10530 \). However, it appears that the provided options don't directly relate to the numerical value obtained from the multiplication of \( 162 \times 65 \).
If you intended for a different format or type of simplification—such as combining or rearranging terms in the expressions—please clarify. Otherwise, if no further instructions are given, the closest simplification would be calculations done stepwise, as shown above.
If you have one particular expression in mind to equate with \( 12x^3y^2 \sqrt{7y} \) and check if \( 162x65 \) fits into any of these simplified forms, let me know!
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