# Express each of the following products as a monomial and verify the result in each case for $x = 1$:$(x^2)^3 \times (2x) \times (-4x) \times 5$

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Given:

$(x^2)^3 \times (2x) \times (-4x) \times 5$

To do:

We have to express the given product as a monomial and verify the result for $x = 1$:

Solution:

$(x^2)^3 \times (2x) \times (-4x) \times 5= x^{2 \times 3} \times 2x \times (-4x) \times 5$

$= x^6 \times 2x \times (-4x) \times 5$

$= 2 \times (-4) \times 5 \times x^{6+1 +1}$

$= -40x^8$

LHS $= (x^2)^3 \times (2x) \times (-4x) \times (5)$

$= (1^2)^3 \times (2 \times 1) \times (-4 \times 1) \times 5$

$= 1^{2 \times 3} \times 2 \times (- 4) \times 5$

$= 1^6 \times 2 \times (-4) \times 5$

$= 1 \times 2 \times (-4) \times 5$

$= -40$

RHS $= -40x^8$

$= -40 \times (1)^8$

$= -40 \times 1$

$= -40$

Therefore,

LHS $=$ RHS

Updated on 10-Oct-2022 13:19:29