Algebra and indices question

[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 :)

 

[CellCoree]

Hi there, it seems like you are using the correct algebraic rule for multiplying expressions with indices. However, the mistake lies in your substitution of values for t. When evaluating expressions with variables, it is important to remember that the values of the variables can change the outcome. In this case, when t=2, you should substitute it into the original expression before simplifying:

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

2(2)^2 x 3(2)^2 = 6(2)^4

2(4) x 3(4) = 6(16)

8 x 12 = 96

So, when t=2, the correct answer is 96, not 20736. I hope this helps clarify your confusion. Remember to always substitute the values into the original expression before simplifying. Keep practicing and you will become more comfortable with indices and algebraic expressions. Good luck!