1 Answer

Chahuistle · Answer 1 · 2022-10-02T04:21:25+0000

Explanation:

$\large\underline{\sf{Given \:Question - }}$

The degree of

$\rm :\longmapsto\:\bigg( - (1)/(20) {x}^(4) {y}^(3)\bigg) * \bigg( - 5 {x}^(7) {y}^(2) \bigg)$

$\green{\large\underline{\sf{Solution-}}}$

Given polynomial is

$\rm :\longmapsto\:\bigg( - (1)/(20) {x}^(4) {y}^(3)\bigg) * \bigg( - 5 {x}^(7) {y}^(2) \bigg)$

can be regrouped as

$\rm \:  =  \: \bigg( - (1)/(20) * ( - 5) \bigg) * \bigg( {x}^(4) * {x}^(7)\bigg) * \bigg( {y}^(3) * {y}^(2) \bigg)$

We know,

$\red{\rm :\longmapsto\:\boxed{\tt{ {x}^(m) \: * \: {x}^(n) \: = \: {x}^(m \: + \: n) \: }}}$

So,

$\rm \:  =  \: (1)/(4) * {x}^(4 + 7) * {y}^(3 + 2)$

$\rm \:  =  \: (1)/(4) * {x}^(11) * {y}^(5)$

$\rm \:  =  \: \frac{ {x}^(11) * {y}^(5) }{4}$

$\rm \:  =  \: \frac{ {x}^(11) \: {y}^(5) }{4}$

Thus,

$\rm :\longmapsto\:\boxed{\tt{ \bigg( - (1)/(20) {x}^(4) {y}^(3)\bigg) * \bigg( - 5 {x}^(7) {y}^(2) \bigg) = \frac{ {x}^(11) \: {y}^(5) }{4} \: }}$

So, Degree of polynomial expression is 16.

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Learn More :-

$\boxed{\tt{ {x}^(m) * {x}^(n) = {x}^(m + n) \: }}$

$\boxed{\tt{ {x}^(m) / {x}^(n) = {x}^(m - n) \: }}$

$\boxed{\tt{ {( {x}^(m)) }^(n) \: = \: {x}^(mn) \: }}$

$\boxed{\tt{ {x}^(0) = 1 \: }}$

$\boxed{\tt{ {x}^( - n) \: = \: \frac{1}{ {x}^(n) } \: }}$