Find the degree of the terms (i) x^2 (ii) 4xyz (iii) 7x^2y^4/xy

Question

Find the degree of the terms

(i) x²

(ii) 4xyz

(iii) \(\frac{7x^2y^4}{xy}\)

(iv) \(\frac{x^2\times\,y^2}{x\times\,y^2}\)

Answer 1

(i) x²

The exponent in x² is 2. 

∴ Degree of the term is 2.

(ii) 4xyz

In 4xyz the sum of the powers of x, y and z as 3.

(iii) \(\frac{7x^2y^4}{xy}\)

We have \(\frac{7x^2y^4}{xy}\) = 7x^2-1 y^4-1 

= 7x¹y³ 

[Since \(\frac{a^m}{a^n}\) = a^m-n]

In 7 x¹ y³ the sum of the powers of x and y is 4(1 + 3 = 4)

Thus degree of the expression is 4.

(iv) \(\frac{x^2\times\,y^2}{x\times\,y^2}\)

We have \(\frac{x^2\times\,y^2}{x\times\,y^2}\) = x^2-1 y^2-2 

= x¹ y⁰ 

= x¹ 

[∵ y⁰ = 1]

The exponent of the expression is 1.