Question

a square has a side length of $x^{2}y^{3}$. what is the area of the square?
$xy - $frightful
$x^{4}y^{9} - $unfriendly
$x^{4}y^{6} - $pleasant
$2x^{2}y^{3} - $glamorous

Explanation:

Step1: Recall the formula for the area of a square

The area \( A \) of a square is given by the formula \( A = s^2 \), where \( s \) is the length of a side.

Step2: Substitute the given side length into the formula

The side length \( s \) is \( x^{2}y^{3} \). So we need to square this expression: \( (x^{2}y^{3})^{2} \).

Step3: Apply the power - of - a - product and power - of - a - power rules

Using the power - of - a - product rule \((ab)^{n}=a^{n}b^{n}\) and the power - of - a - power rule \((a^{m})^{n}=a^{mn}\), we have:
For the \( x \) term: \((x^{2})^{2}=x^{2\times2}=x^{4}\)
For the \( y \) term: \((y^{3})^{2}=y^{3\times2}=y^{6}\)
So \((x^{2}y^{3})^{2}=x^{4}y^{6}\)

Answer:

\( x^{4}y^{6} \) – pleasant