Question

simplify the expression.
$left(\frac{-3r^{4}s^{7}}{r}
ight)^{2}$
$\bigcirc -9r^{6}s^{14}$
$\bigcirc 9r^{6}s^{14}$
$\bigcirc -3r^{6}s^{14}$
$\bigcirc 9r^{3}s^{9}$

Explanation:

Step1: Simplify the base first

$\frac{-3r^4s^7}{r} = -3r^{4-1}s^7 = -3r^3s^7$

Step2: Apply the square exponent

$(-3r^3s^7)^2 = (-3)^2 \cdot (r^3)^2 \cdot (s^7)^2$

Step3: Calculate each term

$(-3)^2=9$, $(r^3)^2=r^{3 \times 2}=r^6$, $(s^7)^2=s^{7 \times 2}=s^{14}$

Step4: Combine the terms

$9 \cdot r^6 \cdot s^{14} = 9r^6s^{14}$

Answer:

$9r^6s^{14}$ (the second option)