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

Given:

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

To do:

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

Solution:

$(5x^4) \times (x^2)^3 \times (2x)^2= 5x^4 \times x^{2\times3} \times 2x \times 2x$

$= 5x^4 \times x^6 \times 4x^2$

$= 5 \times 4 \times x^{4 + 6 + 2}$

$= 20x^{12}$

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

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

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

$= 5 \times 1^6 \times 2^2$

$= 5 \times 1 \times 4$

$= 20$

RHS $= 20x^{12}$

$= 20 (1)^{12}$

$= 20 \times 1$

$= 20$

Therefore,

LHS $=$ RHS

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Updated on: 10-Oct-2022

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