Expert: Scott A Wilson - 6/17/2011

Question
I am on my second semester of algebra in college and need help with a few problems. Thank you very much.

1. Multiply. I got 37 for this one.
(√7+1)(2√7+1)

2. Rewrite with rational exponents.
(^5√(9x^8y)^11

3. simplify. 4 3/2
i got 5.5 for this one.

4. Solve. ∛(2x+9)+8=4
I got x=-73/2 on this one.

Answer
1. Multiply.
(√7+1)(2√7+1)
We need to multiply each term in the first set by the second,
so this can be rewritten as √7(2√7+1) + 1(2√7+1).
This gives 14 + √7 + 2√7 + 1.
The 14 and the 1 can be combined to 15, and the √7 and 2√7 can be combined into 3√7.
This makes the final answer 15 + 3√7.


2. Rewrite with rational exponents: ^5√(9x^8y)^11
If that is suppose to be the 5th root to the 11th, it is known that the 5th root to the 10th is the same as a square with a term left over.  Thus, it is (9x^8y)²√(9x^8y).
Squaring each term gives 81*x^16*y²√(9x^8y).


3. simplify. 4 3/2
You got 5.5 for this one, and that is correct.  Yeah!

4. Solve. ∛(2x+9)+8=4
I got x=-73/2 on this one.
We can subtract 8 from both sides and get 2x+9 = (-4)³ = -64.
I can now see that this is correct as well.  Good job!