How do I simplify 2^(-m) x 3^(-m) x 6^(2m) x 3^(2m) x 2^(2m) as a power of 6?

  • Thread starter Darkmisc
  • Start date
  • Tags
    Indices
In summary, the conversation is about a person asking for help with a math problem for their niece. They have tried to solve it but are stuck at a point where they need to get rid of base 2 and base 3 terms. The solution is 6^(3m) but they are unsure how to get there. They are reminded that 2 times 3 is equal to 6.
  • #1
Darkmisc
204
27
Homework Statement
Write 2^(-m) x 3^(-m) x 6^(2m) x 3^(2m) x 2^(2m) as a power of 6.
Relevant Equations
Write 2^(-m) x 3^(-m) x 6^(2m) x 3^(2m) x 2^(2m) as a power of 6.
Hi everyone

Could someone please help me with a yr 10 maths problem? It's for my niece. I've done 2nd yr uni maths and can't seem to solve it.

Write 2^(-m) x 3^(-m) x 6^(2m) x 3^(2m) x 2^(2m) as a power of 6.

I've attached my attempt in the file. I get stuck at the point where I need to get rid of the base 2 and base 3 terms.

The answer is 6^(3m), but I don't know how to get there. Thanks
 

Attachments

  • WIN_20210204_20_36_28_Pro.jpg
    WIN_20210204_20_36_28_Pro.jpg
    40.3 KB · Views: 94
Physics news on Phys.org
  • #2
Darkmisc said:
I've done 2nd yr uni maths
Then you should know hat ##2\times 3=6## !
 
  • #3
Thanks. It's been a while since I've done maths.
 
  • Like
Likes BvU

1. What is the first step in simplifying this expression?

The first step is to group the like terms together. In this case, we can group the terms with a base of 2 and the terms with a base of 3.

2. How do I simplify the terms with a base of 2?

To simplify the terms with a base of 2, we can use the rule that states when multiplying powers with the same base, we add the exponents. So, 2^(-m) x 6^(2m) x 2^(2m) becomes 2^(-m + 2m + 2m) which simplifies to 2^(3m).

3. What about the terms with a base of 3?

Similarly, for the terms with a base of 3, we can use the same rule and add the exponents. So, 3^(-m) x 3^(2m) becomes 3^(-m + 2m) which simplifies to 3^(m).

4. How do I simplify the remaining terms?

Now that we have simplified the terms with a base of 2 and 3, we are left with 2^(3m) x 3^(m) x 6^(m). To simplify this further, we can use the rule that states when raising a power to another power, we multiply the exponents. So, 6^(m) can be written as (2 x 3)^(m) which becomes 2^(m) x 3^(m). Therefore, our expression becomes 2^(3m) x 3^(m) x 2^(m) x 3^(m).

5. What is the final simplified expression?

Finally, we can use the rule that states when multiplying powers with the same base, we add the exponents. So, our final simplified expression becomes 2^(3m + m) x 3^(m + m) which simplifies to 2^(4m) x 3^(2m). Therefore, the given expression, 2^(-m) x 3^(-m) x 6^(2m) x 3^(2m) x 2^(2m), can be written as a power of 6 as 6^(2m).

Similar threads

  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
10
Views
1K
  • Introductory Physics Homework Help
Replies
15
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Advanced Physics Homework Help
Replies
7
Views
1K
  • Precalculus Mathematics Homework Help
Replies
3
Views
259
  • Introductory Physics Homework Help
Replies
21
Views
2K
  • Introductory Physics Homework Help
Replies
9
Views
2K
  • Introductory Physics Homework Help
Replies
6
Views
5K
Replies
2
Views
183
Back
Top