[tex]\dfrac{(4x^4y^3)^3}{3(5x^2y^6)^2}\qquad\text{use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^{nm}\\\\=\dfrac{4^3(x^4)^3(y^3)^3}{3(5^2)(x^2)^2(y^6)^2}=\dfrac{64x^{12}y^9}{3(25)x^4y^{12}}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\=\dfrac{64}{75}x^{12-4}y^{9-12}=\dfrac{64}{75}x^8y^{-3}=\boxed{\dfrac{64x^8}{75y^3}}[/tex]
[tex]3^{5x-9}=\left(\dfrac{1}{27}\right)^{2x-8}\\\\3^{5x-9}=\left(\dfrac{1}{3^3}\right)^{2x-8}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\3^{5x-9}=(3^{-3})^{2x-8}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\3^{5x-9}=3^{-3(2x-8)}\qquad\text{use distributive property}\\\\3^{5x-9}=3^{(-3)(2x)+(-3)(-8)}\\\\3^{5x-9}=3^{-6x+24}\iff5x-9=-6x+24\qquad\text{add 9 to both sides}\\\\5x=-6x+33\qquad\text{add 6x to both sides}\\\\11x=33\qquad\text{divide both sides by 11}\\\\\boxed{x=3}[/tex]
Chan is not correct. One year has four quarters. Then 7% : 4 = 1.75%.
The equivalent quarterly interest rate would be 1.75% not 2%.
