Question

If the expression (3^(d)*\sqrt(5))/(3^(2)*\sqrt(45)) is equal to 3, what is the value of d

Answer 1

$3^d\cdot\dfrac{\sqrt5}{3^2\cdot\sqrt{45}}=3\\\\\dfrac{3^d\sqrt5}{3^2\sqrt{9\cdot5}}=3\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\\dfrac{3^d\sqrt5}{3^2\sqrt9\cdot\sqrt5}=3\\\\\dfrac{3^d}{3^2\cdot3}=3\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\\dfrac{3^d}{3^{2+1}}=3\\\\\dfrac{3^d}{3^3}=3\qquad\text{multiply both sides by}\ 3^3\\\\3^d=3\cdot3^3\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\3^d=3^{1+3}\\\\3^d=3^4\iff\boxed{d=4}$