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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Updated on: 10-Oct-2022

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