- #1

hackedagainanda

- 52

- 11

- Homework Statement
- Simplify and remove all negative exponents from this equation:

## \frac {2k^2 k^3} {k^{-1} k^{-5}}(5k^{-2})^{-3}##

- Relevant Equations
- Quotient Rule: ##\frac {x^a} {x^b} = x^{a-b}##

Product Rule: ## x^a x^b = x^{a+b}##

So my attempt is this: ##(2k)^2 k^3 = 4k^5## to clear the top numerator then to clear the denominator ## k^{-1} k^{-5} = k^{-6}##Then I apply the quotient rule and get ##4k^{11} (5k^{-2})^{-3}## and simplifying the right hand side I get ##5^{-3} k^6## here is where I got lost, why is it that when you use a negative exponent on the 5 to get 1/125 why do you apply the ##k^{17}## to numerator and not the denominator ##\frac {4k^{17}} {125}## Why isn't the answer ## \frac {4} {125k^{17}}## ?

I probably forgot the rules from arithmetic most likely, I feel embarrassed to ask but that's the only way you learn.

I probably forgot the rules from arithmetic most likely, I feel embarrassed to ask but that's the only way you learn.