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