Question

What is the degree of the expression $\frac{5\cdot x^{\frac{2021}{2022}}}{x^{\frac{2021}{2022}}}?$

• A. $0$
• B. $1$
• C. $2021$
• D. $2022$

Answer 1

The correct option is A $0$

$\underset{–}{\text{Need to Find:}}$
Degree of the expression $\frac{5\cdot x^{\frac{2021}{2022}}}{x^{\frac{2021}{2022}}}$

Because the given expression is not in standard form, we'll simplify it and express it in standard form first.

$\frac{5\cdot x^{\frac{2021}{2022}}}{x^{\frac{2021}{2022}}}$

$=5\cdot x^{\frac{2021-2021}{2022}}$ $[\because \frac{a^m}{a^n}=a^{(m-n)}]$

$=5\cdot x^0$

As a result, given expression is simplified to $\underset{–}{5x^0}.$

Now, as we know, the largest power of the variable is the degree of the polynomial. Here, the largest power of the variable $\underset{–}{x}$ is $\underset{–}{0}.$ Therefore, degree of the given polynomial is $\underset{–}{0}.$

Hence, option (a.) is the correct one.

$\underset{–}{\text{Note:}}$
Degree of a non-zero constant polynomial is always $0.$