divide and simplify .
1. 5x^4/3 divided by 5x^2/6
2. 3/a^5 divided by 3/a^2
3. 6m^4/5 divided by 2m
Can someone help me do these? and explain them? because I don't understand how to do them. thanks.
isn't #1 2x^2?
and then #2 is 1/a^3?
3/a^5 divided by 3/a^2
3/a^5
--------
3/a^2
multiply top and bottom by a^5
3
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3 a^3
so yes a^-3 or 1/a^3
6m^4/5 divided by 2m
3 m^3/5 or (3/5) m^3
thanks!
Sure! I'd be happy to help you with these problems and explain how to solve them.
1. To divide and simplify the expression (5x^4/3)/(5x^2/6), we can follow these steps:
- The division of two fractions can be solved by multiplying the first fraction by the reciprocal of the second fraction.
- The reciprocal of a fraction "a/b" is simply "b/a".
- In this case, we have (5x^4/3)/(5x^2/6). To find the reciprocal of 5x^2/6, we flip it and get 6/(5x^2).
- Now, we can multiply the first fraction by the reciprocal of the second fraction: (5x^4/3) * (6/(5x^2)).
- To multiply fractions, we multiply the numerators together and the denominators together: (5 * 6 * x^4) / (3 * 5 * x^2).
- Simplifying, we get (30x^4) / (15x^2).
- Finally, we can simplify further by dividing both the numerator and denominator by 15x^2: 2x^2.
2. To divide and simplify the expression (3/a^5)/(3/a^2), we can follow a similar approach:
- Again, the division of two fractions can be solved by multiplying the first fraction by the reciprocal of the second fraction.
- The reciprocal of 3/a^2 is a^2/3.
- So, we have (3/a^5) * (a^2/3).
- Multiplying the numerators and the denominators: (3 * a^2) / (a^5 * 3).
- Simplifying further, we can cancel out one "3" from numerator and denominator: a^2 / a^5.
- Now, to simplify a^2 / a^5, we subtract the exponents since the bases are the same: a^(2-5) = a^(-3).
- Finally, we can rewrite a^(-3) as 1/a^3. Therefore, the simplified expression is 1/a^3.
3. To divide and simplify the expression (6m^4/5)/(2m), we can follow the same method:
- The reciprocal of 2m is 1/(2m).
- So, we have (6m^4/5) * (1/(2m)).
- Multiplying the numerators and the denominators: (6m^4 * 1) / (5 * 2m).
- Simplifying, we get (6m^4) / (10m).
- We can further simplify by canceling out a common factor of 2 between the numerator and denominator: (3m^4) / (5m).
- And finally, we can cancel one "m" from numerator and denominator, resulting in (3m^3) / 5.
I hope this helps! Remember, understanding the steps behind the solution is important for mastering these concepts. Let me know if you have any further questions.