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Question

Express each of the following product as a monomials and verify the result in each case for x = 1:
(x2)3 × (2x) × (−4x) × (5)

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Solution

We have to find the product of the expression in order to express it as a monomial.

To multiply algebraic expressions, we use commutative and associative laws along with the laws of indices, i.e.,​am×an=am+n and amn=amn .

We have:

x23×2x×-4x×5=x6×2x×-4x×5=2×-4×5×x6×x×x=2×-4×5×x6+1+1=-40x8

x23×2x×-4x×5=-40x8

Substituting x = 1 in LHS, we get:​

LHS =x23×2x×-4x×5=123×2×1×-4×1×5=16×2×-4×5=1×2×-4×5=-40

Putting x = 1 in RHS, we get:​

RHS=-40x8=-4018=-40×1=-40

LHS = RHS for x = 1; therefore, the result is correct

Thus, the answer is -40x8.

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