the area of a square can be represented by the expression $x^{10}$. which monomial represents a side of the…

the area of a square can be represented by the expression $x^{10}$. which monomial represents a side of the square?\n$x^{2}$\n$x^{5}$\n$x^{20}$\n$x^{100}$

the area of a square can be represented by the expression $x^{10}$. which monomial represents a side of the square?\n$x^{2}$\n$x^{5}$\n$x^{20}$\n$x^{100}$

Answer

Explanation:

Step1: Recall area formula for square

The area $A$ of a square is $A = s^2$, where $s$ is the side - length of the square. Given $A=x^{10}$, we need to find $s$ such that $s^2=x^{10}$.

Step2: Use exponent rule for square - root

If $s^2 = x^{10}$, then $s=\sqrt{x^{10}}$. According to the rule $\sqrt{a^m}=a^{\frac{m}{2}}$ (for $a\geq0$), when $a = x$ and $m = 10$, we have $s=x^{\frac{10}{2}}$.

Step3: Simplify the exponent

$x^{\frac{10}{2}}=x^5$.

Answer:

B. $x^5$