SOLUTION: I tried, actually I have no idea how to solve this problem. Please help me solve this problem: EXPONENTS: Simplify. #23. {{{5^(3n+6)=(5^(2n))(5^(4n-6))}}} Please and Than

Algebra ->  Algebra  -> Formulas -> SOLUTION: I tried, actually I have no idea how to solve this problem. Please help me solve this problem: EXPONENTS: Simplify. #23. {{{5^(3n+6)=(5^(2n))(5^(4n-6))}}} Please and Than      Log On

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Question 88345: I tried, actually I have no idea how to solve this problem. Please help me solve this problem:
EXPONENTS:
Simplify.
#23. 5%5E%283n%2B6%29=%285%5E%282n%29%29%285%5E%284n-6%29%29
Please and Thank you!!!!
Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for n:
5%5E%283n%2B6%29+=+%285%5E%282n%29%29%285%5E%284n-6%29%29 On the right side side, apply the rule of exponents:%28a%5En%29%28a%5Em%29+=+a%5E%28n%2Bm%29
5%5E%283n%2B6%29+=+5%5E%282n%2B4n-6%29 Simplify.
5%5E%283n%2B6%29+=+5%5E%286n-6%29 Apply the rule: Ifa%5En+=+a%5Em then: n+=+mfor any positive a not = 1
3n%2B6+=+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%5E%283%284%29%2B6%29+=+%285%5E%282%284%29%29%29%285%5E%284%284%29-6%29%29 Simplify.
5%5E18+=+%285%5E8%29%285%5E10%29
5%5E18+=+5%5E18