Question

What is the degree of the polynomial $y^2(y^5{)}^2$ ?

• A. $10$
• B. $9$
• C. $12$
• D. $7$

Answer 1

The correct option is C $12$

We are given with a polynomial expression $y^2(y^5{)}^2$.

The polynomial expression $y^2(y^5{)}^2$ can be simplified as:

$y^2(y^5{)}^2=y^2(y^{5\times 2})$ (Since $(a^m{)}^n=a^{mn}$)

$=y^2\left(y^{10}\right)$
$=y^{2+10}$ (Since $a^m\times a^n=a^{m+n}$)
$=y^{12}$
$y^2(y^5{)}^2=y^{12}$

The polynomial expression $y^2(y^5{)}^2$ after simplification can be written as $y^{12}$. The degree of the polynomial expression $y^{12}$ is $12$.

Hence, we can say that the degree of the polynomial expression $y^2(y^5{)}^2$ is $12$.

Therefore, option (c.) is the correct answer.