Why Do I Get Different Results When Calculating Powers and Indices?

[peterspencers]

Hi there, I am stuck, please can someone help me to understand where I am going wrong...

I have been learning about indices and i am confused.. here is an example of why..

2t squared x 3t squared = 6t power 4

but if i give t a value of 2..

2x2 squared = 16

3x2 squared = 36

16 x 36 = 576

but... 6x2 power 4 = 20736

why am i getting two different answers, what am I doing wrong?

 

[sgfw]

(2*t)^2*(3*t)^2 is not the same thing as (6*t)^4 because if I expand them out, it comes out to be 36*t*t*t*t instead of (2*t)^2*(3*t)^2, and (6*t)^4 is 1296*t*t*t*t, which obviously do not equal each other unless t = 0.

I think you may be grouping them wrong, because if you simply move the parenthesis, you get 2*(t^2)*3*(t^2) = 6*(t^4) which is true because 2*(t^2)*3*(t^2) is the same thing as saying 6*t*t*t*t: I just multiplied the 3 and 2, and expanded the t^2's. 6*(t^4) is the same thing as saying 6*t*t*t*t as well, for the same reason, therefore they must equal each other.

If you are confused by the notation I am using, * means multiply, and ^ means to the power of.

 

[Mark44]

Hi there, I am stuck, please can someone help me to understand where I am going wrong...

I have been learning about indices and i am confused.. here is an example of why..

2t squared x 3t squared = 6t power 4

There are better ways to represent what we in America call exponents.
1. Simplest - Use ^, which is notation that comes from the Basic programming language.
Your problem would appear as 2t^2 * 3t^2 = 6t^4
2. HTML tags - Click the Go Advanced button below the text input area. This causes the advanced menu to show across the top of the entry pane. The X² button inserts tags around your exponent.
Your problem now looks like this: 2t² * 3t² = 6t⁴.
3. LaTeX script - I won't go into detail about how to do this, but you can find out more in this post: https://www.physicsforums.com/showpost.php?p=3977517&postcount=3.
With LaTeX script your equation looks like this:
$2t^2 \cdot 3t^2 = 6t^4$
If you right-click on what I wrote, you can see the script that did it.

but if i give t a value of 2..

2x2 squared = 16

3x2 squared = 36

No to both. If t = 2, then 2t² = 2 * 2² = 8, and 3t² = 3 * 2² = 12.
So when t = 2, 2t² * 3t² = 8 * 12 = 96.

On the other hand, 6t⁴ = 6 * 2⁴ = 6 * 16 = 96.

16 x 36 = 576

but... 6x2 power 4 = 20736

why am i getting two different answers, what am I doing wrong?

Instead of squaring just the variable (i.e., 2t²), you are squaring the whole thing, (2t)²). These are different. Same for the other factor, 3t².

 

[peterspencers]

Thankyou so much :)