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(\sqrt5)/(3^2\cdot√(45))=3\\\\(3^d\sqrt5)/(3^2√(9\cdot5))=3\qquad\text{use}\ √(ab)=√(a)\cdot√(b)\\\\(3^d\sqrt5)/(3^2\sqrt9\cdot\sqrt5)=3\\\\(3^d)/(3^2\cdot3)=3\qquad\text{use}\ a^n\cdot a^m=a^(n+m)\\\\(3^d)/(3^(2+1))=3\\\\(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}`