indices, a level maths, how do i work out the answers to these 2 questions? x^2 divide x^-1/x^2, and x/x^-4?

Answer 1

x^-1 / x^2 = x^-3

When you divide bases to different powers (if the base is the same) you subtract the exponents. Multiplying common bases is adding exponents.

64 * 4 = 256

2^6 * 2^2 = 2^8

so, the second is x^5

Answer 2

When dividing, subtract the indices.
When dividing by a fraction,invert fraction and multiply
Example
(3/4)/(5/8) becomes 3/4 x 8/5=24/20 = 6/5
Thus in questions given:-

Qu. 1
x²/(x^(-1)/x^(-2) = X² x X-² x 1/X^(-1) = 1/X^(-1) = X


Qu.2
X/(X^(-4) = X x X^4 = X^5

Answer 3

x^2 / x^-1/x^2 i think is the first question i think you said, not sure
same as x^2 * x^2/x^-1 then x^4/x^-1 which makes x^5

when multiplying, add the powers, when dividing, subtract the powers

x/x^-4 makes x^5 because you do 1- -4 = 5

good luck

Answer 4

x^2 divide x^-1/x^2 = x^2/x^(-1-2) = x^2/x^(-3) = x^(2--3) = x^(2+3) = x^5

x/x^-4 = x^(1--4) = x^(1+4) = x^5

Answer 5

Not sure exactly what the question is - the first x^2 seems to be redundant. However, for indices you just have to remember 3 basic rules and the rest is easy.
(x^a) x (x^b) = x^(a+b)
(x^a)/(x^b) = x^( a-b)
(x^a)^b = x^(axb)
Hence x^-1/x^2 = x^-3 or 1/x^3
& x/x^-4 = x^5

Hope that's what you wanted