I am taking a practice math test in preparation for attendance of a university. The test they sent me has the answers in the back to compare your answers to once you've completed it, and if they're wrong to figure out why and correct it. I'm having trouble with a couple of questions. I was wondering if someone would mind doing a step-by step work-through of this problem:
48a^-4b^6/144a^5b^-3
Also, I had (3a^2b/2ab^-3)^3 as a question. I completed it and got the answer 27a^3b^12/8. The answer given at the back of the test is 27/8 a^3b^12. Both answers are equatable, but I was wondering if the way that the answer was written was a more "proper" way to write it, and if so, why.
48a^-4b^6/144a^5b^-3
Also, I had (3a^2b/2ab^-3)^3 as a question. I completed it and got the answer 27a^3b^12/8. The answer given at the back of the test is 27/8 a^3b^12. Both answers are equatable, but I was wondering if the way that the answer was written was a more "proper" way to write it, and if so, why.
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48(a^-4)(b^6)/144(a^5)(b^-3)
When you have a negative exponent in the numerator of a fraction, you can bring the term down to the denominator and make the exponent positive. When you have a negative exponent in the denominator of a fraction, you can bring the term up to the numerator and make the exponent positive:
48(b^6)(b^3)/144(a^5)(a^4)
Now simplify:
(48b^9)/144a^9
(b^9)/3a^9
For your other question, if you write the numerator all on one line and the denominator underneath it, then it's easy to understand what you mean. If you write it exactly as you have it in your question, it's hard to tell where the 8 is, (Is it dividing the exponent on b?) and it's easier to understand the way they have it.
When you have a negative exponent in the numerator of a fraction, you can bring the term down to the denominator and make the exponent positive. When you have a negative exponent in the denominator of a fraction, you can bring the term up to the numerator and make the exponent positive:
48(b^6)(b^3)/144(a^5)(a^4)
Now simplify:
(48b^9)/144a^9
(b^9)/3a^9
For your other question, if you write the numerator all on one line and the denominator underneath it, then it's easy to understand what you mean. If you write it exactly as you have it in your question, it's hard to tell where the 8 is, (Is it dividing the exponent on b?) and it's easier to understand the way they have it.