Question

simplify the following expression. if the answer contains exponer
$left( dfrac{6x^{2}y^{-2}}{3x^{4}y^{-4}}
ight)^{-3} = square$
question help: video ebook message instructor

Explanation:

Step1: Simplify coefficients first

$\frac{6}{3} = 2$

Step2: Simplify $x$-terms (subtract exponents)

$x^{2-4} = x^{-2}$

Step3: Simplify $y$-terms (subtract exponents)

$y^{-2-(-4)} = y^{2}$

Step4: Apply outer exponent to all terms

$(2x^{-2}y^{2})^{-3} = 2^{-3}x^{(-2)(-3)}y^{(2)(-3)}$

Step5: Compute each simplified term

$2^{-3}=\frac{1}{8}$, $x^{6}$, $y^{-6}=\frac{1}{y^6}$

Step6: Combine all terms

$\frac{1}{8} \cdot x^6 \cdot \frac{1}{y^6} = \frac{x^6}{8y^6}$

Answer:

$\frac{x^6}{8y^6}$