1. ## Pascal's Triangle

Suppose b is an integer with b >= 7. Use the Binomial Theorem and the appropriate row of Pascal's triangle to find the base-b expansion of ((11)b)^4 (that is, the fourth power of the number (11)b in base b notation).

I don't understand what exactly the question is asking. Do I need to write out a particular row of Pascal's triangle? What is meant by the base b notation? No row of Pascal's triangle contains 11^4 = 14641 in it, so what is meant by the fourth power? Thanks much.

2. Hello, aaronrj!

I had to read it twice to catch on . . .

Suppose $\displaystyle b$ is an integer with $\displaystyle b \geq 7$.
Use the Binomial Theorem and the appropriate row of Pascal's triangle
to find the base-b expansion of $\displaystyle (11_b)^4$
(that is, the fourth power of the number $\displaystyle 11_b$ in base b notation).
We are expected to be familiar with number bases.

For example, $\displaystyle 3104_5$ means: $\displaystyle 3\!\cdot\!5^3 + 1\!\cdot\!5^2 + 0\!\cdot\!5 + 4\!\cdot\!1 \:=\:104$

Then we see that: .$\displaystyle 11_b$ means: .$\displaystyle 1\!\cdot\!b + 1 \;=\;b + 1$

And they are asking for: .$\displaystyle (b + 1)^4$

. . Got it?