Simplify and verify the result for $p=1$.$4 p^{3} \times 3 p^{4} \times( -p^{5})$
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Given: $4p^{3}\times 3p^{4}\times( -p^{5})$

To do: Simplify and verify the result for $p=1$.

Solution:

$4p^{3}\times 3p^{4}\times( -p^{5})$

$\Rightarrow 4p^{3}\times 3p^{4}\times( -p^{5})=4\times3\times p^{3}\times p^{4}\times p^{5}$

$\Rightarrow 4p^{3}\times 3p^{4}\times( -p^{5})=-12p^{3+4+5}$                               [$\because a^m\times a^n=a^{m+n}$]

$\Rightarrow 4p^{3}\times 3p^{4}\times( -p^{5})=-12p^{12}$

Verification:

$L.H.S.=4p^{3}\times 3p^{4}\times( -p^{5})$

$=4\times 1^3\times 3\times1^4\times ( -1^5)$

$=-12$

$R.H.S.=-12p^{12}$

$=-12\times 1^{12}$

$=-12$

Thus, $L.H.S.=R.H.S.$, verified.

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Updated on: 10-Oct-2022

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