Find the degree of the terms(i) x2(ii) 4xyz(iii) \(\frac{7x^2y^4}{xy}

1.	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» (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 x¹y³ 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.

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»

(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 x¹y³ 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.