Question 88345
Solve for n:
{{{5^(3n+6) = (5^(2n))(5^(4n-6))}}} On the right side side, apply the rule of exponents:{{{(a^n)(a^m) = a^(n+m)}}} 
{{{5^(3n+6) = 5^(2n+4n-6)}}} Simplify.
{{{5^(3n+6) = 5^(6n-6)}}} Apply the rule: If{{{a^n = a^m}}} then: {{{n = m}}}for any positive a not = 1
{{{3n+6 = 6n-6}}} Subtract 3n from both sides.
{{{6 = 3n-6}}} Add 6 to both sides.
{{{12 = 3n}}} Divide both sides by 3.
{{{n = 4}}}
Check by substituting n = 4 into the original equation.
{{{5^(3(4)+6) = (5^(2(4)))(5^(4(4)-6))}}} Simplify.
{{{5^18 = (5^8)(5^10)}}}
{{{5^18 = 5^18}}}