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Express each of the following products as a monomial and verify the result for $x = 1,y = 2$:
$(-xy^3) \times (yx^3) \times (xy)$
Given:
$(-xy^3) \times (yx^3) \times (xy)$
To do:
We have to express the given product as a monomial and verify the result for $x = 1,y = 2$.
Solution:
$(-xy^3) \times (yx^3) \times (xy)=-x \times x^3 \times x \times y^3 \times y \times y$
$= -x^{1 + 3 + 1} \times y^{3 + 1 + 1}$
$= -x^5y^5$
LHS $= (-xy^3) \times (yx^3) \times (xy)$
$= (-1 \times 2^3) \times (2 \times (1)^3) \times (1 \times 2)$
$= (-1 \times 8) \times (2 \times 1) \times (1 \times 2)$
$= -8 \times 2 \times 2$
$= -32$
RHS $=-x^5y^5$
$= -(1)^5 \times (2)^5$
$= -1 \times 32$
$=-32$
Therefore,
LHS $=$ RHS
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