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2. a) For which bases b is (1331)6 the cube of an integer? (b) Find the base b if (100)6 (30)6 (4A)11, where A is the base 11 digit that represents the number ten F...

Question

2. a) For which bases b is (1331)6 the cube of an integer? (b) Find the base b if (100)6 (30)6 (4A)11, where A is the base 11 digit that represents the number ten Find € if (2x3)4 (1x10)3.

2. a) For which bases b is (1331)6 the cube of an integer? (b) Find the base b if (100)6 (30)6 (4A)11, where A is the base 11 digit that represents the number ten Find € if (2x3)4 (1x10)3.



Answers

Find the value of the base $b$ in each case.
$$
1001_{b}=9
$$

Hi, everyone. So today's problem says the number A is the cube root of a number. Be if a to the Q Cube equals B. For example. The Q brew of eight is, too, because to cubed equals eight. Could you have two times two, which is four and then four Chemistry, which is eight by the Cuba in reach number. So a. We have 64. Well, the cubit of this is for because we have four Tom's four, which equals 16. And then Tom's Whore gives us 64 be the cube root of 1000 is turn because turn comes turn gives us 100 times 10. Gives us 1000 for the cubed root. Ah, 343. It is seven. So we have seven times seven gives us 49. Toms seven gives us 343 and a cute root of 2197 is 13. We have 13 times 13 which gives us 160 round that we will live out by 13 and we get 2197. So these are the cube root of each of you

My guys. So a number 16 were asked to identify the experiment on the base. So our basis or bottom sweep inside the parentheses raised three on the bottom is 13 case That's going to be our base sits on the bottom on 13 k is raised to the power three, which is our exponents. Three is also a night bird times that 13 acts will be multiplied by itself. Our export industry basis 13.

We were asked to identify the exponents, and the base base is bottom is how I always remember. So in parentheses we have negative 11 a. On top. We have to swim bottom. We have negative 11 A. Which means that will be our base and our exponents is on top, which is to which means negative. 11. A will be multiplied by itself two times. It's going to be negative. 11. A time started. 11 A. There's too negative 11 8th

Okay. You may be a little bit tricky to understand what this question is asking. So first observed that 11 with that small be on the bottom means that we are talking about the number that can be written us one time speed. Bless one. Okay, so each one off these terms, the 1st 1 would mean there p to the zero. The 2nd 1 will mean B to the one. The 3rd 1 if they were there, will mean be square. Okay, so we're working with a number B plus one. Now we have to calculate that number to the fore and bye bye. The binomial theorem. Thatis expression off that expansion. And so, calculating those numbers, we get Pete to the four plus for between three plus six b square plus four b plus one. So I said, What's saying before we want to rewrite that in that shape. So the coefficient that goes we be to the four will be the 1st 1 Then be 234 Then be square seats, then before we go there and then one. And that east expansion ist expression in the based be off 11 in the base B to the fore


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