Exponants and radicals

[Anotherstudent]

Hi people, please I could use some help with this following math problem.
I have to simplify and express the next expression without any negative exponants.

8^-3a^-1c² multiply by (1/2)⁴ac^-3

I know the answer is 2^13c but I can't figure how the heck to get there. Tyvm for your help

 

[HallsofIvy]

Hi people, please I could use some help with this following math problem.
I have to simplify and express the next expression without any negative exponants.

8^-3a^-1c² multiply by (1/2)⁴ac^-3

I know the answer is 2^13c but I can't figure how the heck to get there. Tyvm for your help

You get rid of the negative exponents by writing them as denominators of fractions: \(\displaystyle 8^{-3}a^{-1}c^2= \dfrac{c^2}{8^3a}\) and \(\displaystyle (1/2)^4ac^{-3}= \dfrac{a}{2^4c^3}\). Multiply those. (It is \(\displaystyle \dfrac{1}{2^{13}c}\) NOT \(\displaystyle 2^{13}c\).)