((((maths help needed.))))?

Question:Simplify this question, giving your answer in positive index only.

Q1) 2a^-5 / 7b^-5

Please give detailed working so that I will understand.

Thank you very much for your help.

Answers:
Keep in mind that a negative exponent MOVES THE BASE from numerator to denominator or denominator to numerator, like an elevator. Then the exponent becomes positive.

So, 2a^-5/ 7b^-5

becomes 2b^5/7a^5.

If there were () around them, such as (2a)^-5, the 2 would have to move also and be taken to the 5th power. In other words, if it were,

(2a)^-5/(7b)^-5 you would get

(7^5)b^5 / 32a^5.
what's the topic of your question?

i think, it's already simplified. because you cannot cancel a and b.
look at my solution to know and understand it that we cannot cancel unsimilar terms or numbers/letters.

2a^5/7b^5 = 2 (a)(a)(a)(a)(a) / 7 (b)(b)(b)(b)(b)

we cannot divide 2 and 7.so, leave it in rational form: 2/7.
the exponent 5 means we are going to multiply the base 2 and 7 five times itself.

there is no more simplification for that.
but if we are going to answer this type of question:

4a^5 / 2a^2

then, we can simplify it.

try to expand the equation:

4(a)(a)(a)(a)(a) / 2(a)(a)

4 divided by 2 is 2.
then, we are going to pair two a to cancel it and get the final exponent. so, 5a -2a= 3a

try to cancel them on your paper and you can see that there will be only 3a left.

or, in mathematical form, 5-2 = 3.
or raise the exponent of the denominator and reverse its sign.( + to - ).

hope this helps!

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