r^3r^-4/4^-2r^-5 i tried doing r^3/r^-2 x r-4/r-5 & got r^5,r^1 but the answer is r6, what am i doing wrong?

I will interpret your r^3r^-4/4^-2r^-5 as

r^3 r^-4/(4^-2 r^-5)
= r^-1/(...... wait, is that 4^-2 supposed to be r^-2 ???

anyway, if you got r^5 r^1, isn't that r^6 ???
(why is there a comma in r^5 r^1 ? )

the problem is r^3r^4/r^-2r^-5

then take a look at what you first typed.

ok then:
r^3r^4/r^-2r^-5
= r^(3+4-(-2)-5)
= r^4

if you meant:
r^3r^4/(r^-2r^-5)

= r^7 / r^-7
= r^(7-(-7))
= r^14

to get r^6 as an answer the question would have been

r^3 r^-4/(r^-2 r^-5) , and that is not what you typed.

i meant the last problem you typed

in that case, the problem is very straightforward

r^3 r^-4/(r^-2 r^-5)
= r^-1/r^-7
= r^(-1 - (-7))
= r^6

To simplify the expression r^3 * r^-4 / 4^-2 * r^-5, let's break it down step by step.

Step 1: Simplify the numerator.
r^3 * r^-4 = r^(3 + (-4)) = r^(-1) = 1/r^1 = 1/r

So, the numerator simplifies to 1/r.

Step 2: Simplify the denominator.
Since 4^-2 = 1/4^2 = 1/16, the denominator becomes 1/16.

Now, the expression becomes (1/r) / (1/16) * r^-5.

Step 3: Simplify further.
To divide by a fraction, we multiply by its reciprocal. So, we can rewrite the expression as:
(1/r) * (16/1) * r^-5.

Multiplying the numerators and denominators, we get:
(16 * 1) / (1 * r) * r^-5 = 16 / (r * r^-5).

Step 4: Combine the variables with exponents.
Using the rule a^b/a^c = a^(b-c), we can simplify the expression further.
16 / (r * r^-5) = 16 / (r^(1 + (-5))) = 16 / r^(-4) = 16r^4.

Therefore, the simplified expression is 16r^4, not r^6.

It seems like you made an error in Step 1 when simplifying the numerator. Instead of getting r^1, you should have used the rule a^(-n) = 1/a^n to simplify r^(-1) to 1/r^1 = 1/r.

Remember to be careful with the signs and exponents during simplification to get the correct result.