Question

Solve and Explain this​

Answer 1

Answer:

degree is 16.

Step-by-step explanation:

first multiply both algebraic expressions

the find the sum of the power of variables.

Answer 2

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

The degree of

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

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

Given polynomial is

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

can be regrouped as

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

We know,

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

So,

$\rm \:  =  \: \dfrac{1}{4} \times {x}^{4 + 7} \times {y}^{3 + 2}$

$\rm \:  =  \: \dfrac{1}{4} \times {x}^{11} \times {y}^{5}$

$\rm \:  =  \: \dfrac{ {x}^{11} \times {y}^{5} }{4}$

$\rm \:  =  \: \dfrac{ {x}^{11} \: {y}^{5} }{4}$

Thus,

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

So, Degree of polynomial expression is 16.

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Learn More :-

$\boxed{\tt{ {x}^{m} \times {x}^{n} = {x}^{m + n} \: }}$

$\boxed{\tt{ {x}^{m} \div {x}^{n} = {x}^{m - n} \: }}$

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

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

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