Step-by-step explanation:
[tex]\large\underline{\sf{Given \:Question - }}[/tex]
The degree of
[tex]\rm :\longmapsto\:\bigg( - \dfrac{1}{20} {x}^{4} {y}^{3}\bigg) \times \bigg( - 5 {x}^{7} {y}^{2} \bigg) [/tex]
[tex]\green{\large\underline{\sf{Solution-}}}[/tex]
Given polynomial is
[tex]\rm :\longmapsto\:\bigg( - \dfrac{1}{20} {x}^{4} {y}^{3}\bigg) \times \bigg( - 5 {x}^{7} {y}^{2} \bigg) [/tex]
can be regrouped as
[tex]\rm \: = \: \bigg( - \dfrac{1}{20} \times ( - 5) \bigg) \times \bigg( {x}^{4} \times {x}^{7}\bigg) \times \bigg( {y}^{3} \times {y}^{2} \bigg) [/tex]
We know,
[tex]\red{\rm :\longmapsto\:\boxed{\tt{ {x}^{m} \: \times \: {x}^{n} \: = \: {x}^{m \: + \: n} \: }}}[/tex]
So,
[tex]\rm \: = \: \dfrac{1}{4} \times {x}^{4 + 7} \times {y}^{3 + 2} [/tex]
[tex]\rm \: = \: \dfrac{1}{4} \times {x}^{11} \times {y}^{5} [/tex]
[tex]\rm \: = \: \dfrac{ {x}^{11} \times {y}^{5} }{4} [/tex]
[tex]\rm \: = \: \dfrac{ {x}^{11} \: {y}^{5} }{4} [/tex]
Thus,
[tex]\rm :\longmapsto\:\boxed{\tt{ \bigg( - \dfrac{1}{20} {x}^{4} {y}^{3}\bigg) \times \bigg( - 5 {x}^{7} {y}^{2} \bigg) = \frac{ {x}^{11} \: {y}^{5} }{4} \: }}[/tex]
So, Degree of polynomial expression is 16.
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Learn More :-
[tex]\boxed{\tt{ {x}^{m} \times {x}^{n} = {x}^{m + n} \: }}[/tex]
[tex]\boxed{\tt{ {x}^{m} \div {x}^{n} = {x}^{m - n} \: }}[/tex]
[tex]\boxed{\tt{ {( {x}^{m}) }^{n} \: = \: {x}^{mn} \: }}[/tex]
[tex]\boxed{\tt{ {x}^{0} = 1 \: }}[/tex]
[tex]\boxed{\tt{ {x}^{ - n} \: = \: \frac{1}{ {x}^{n} } \: }}[/tex]
