HIVE: Math question help, please

[TheApprentice]

Math question for Ds: Write 36 to the power of 11 as a power of 6.

 

Answer: 6 to the power of 22.

 

How?:confused:

 

I wish I was better at math, seriously.

[Ailaena]

36^11 = (6^2)^11 = 6^(2*11) = 6^22

 

its the multiplication power rule, but you have to recognize that 36 can be converted to 6^2.

[2cents]

For this, I personally would start using the process of elimination. The answer for both is 1.316 so they just want to know what power of 6 to use if you want the same answer you get with the problem of 36 with an exponent of 11 (1.316). They could just ask, 'to get the answer 1.316 to what power would you have to raise 6?

 

So, this is where I would just use the process of elimination to come up with the correct answer...unless there is a formula. Maybe another poster can help with that?

[regentrude]

For this, I personally would start using the process of elimination. The answer for both is 1.316 so they just want to know what power of 6 to use if you want the same answer you get with the problem of 36 with an exponent of 11 (1.316). They could just ask, 'to get the answer 1.316 to what power would you have to raise 6?

 

So, this is where I would just use the process of elimination to come up with the correct answer...unless there is a formula. Maybe another poster can help with that?

 

Elimination helps to solve one particular problem - but it does not teach the necessary skill!

There are formulas which the students need to know: the basic laws of exponents: (a^b)^c= a^(b*c)

 

so 36^11= (6^2)^11= 6^(11*2)=6^22

 

btw, how do you come up with 1.316? If you multiply 36 eleven times by itself, you get 1.316*10^17

 

The student needs to be able to solve this completely without a calculator - because soon the numbers might well be replaced by variable and a calculator will be useless.

Edited February 26, 2011 by regentrude

[2cents]

Elimination helps to solve one particular problem - but it does not teach the necessary skill!

There are formulas which the students need to know: the basic laws of exponents: (a^b)^c= a^(b*c)

 

so 36^11= (6^2)^11= 6^(11*2)=6^22

 

btw, how do you come up with 1.316? If you multiply 36 eleven times by itself, you get 1.316*10^17

 

The student needs to be able to solve this completely without a calculator - because soon the numbers might well be replaced by variable and a calculator will be useless.

 

I've always been an advocate of mastering the why and how. That is why I specifically stated that maybe some other wtm poster could explain that. You must have missed that part of my post. As for your question about how I came up with 1.316. That is what you get when you 'round' off the answer. 1.316*10^17 is what you get when you use a calculator (or more specifically: 1.316217e+17). ;)

Edited February 26, 2011 by 2cents

[TheApprentice]

Thank you so much regentrude and Ailaena. This is why we are not continuing with Kinetic Books next year. Just not enough explanation for us non-mathy types.

[Dana]

I've always been an advocate of mastering the why and how. That is why I specifically stated that maybe some other wtm poster could explain that. You must have missed that part of my post. As for your question about how I came up with 1.316. That is what you get when you 'round' off the answer. 1.316*10^17 is what you get when you use a calculator (or more specifically: 1.316217e+17). ;)

 

I don't mean to slam, but this is a very serious misunderstanding.

10^17 is a 1 with 10 zeros, so 1.316 *10^17 =

131,600,000,000,000,000

 

While I can easily have $1.316, I'll never see $1.316*10^17.

 

You can't just drop the place value (10^17).

 

The exponential rules continue to appear in almost every math course beyond algebra & they're what give many students a tremendous amount of difficulty.