(xy^3z^4)(x^-4y^-3z^-1) can anyone explain how to solve this step by step?

Question

I have the answer to the problem but unfortunately I do not understand how to solve it. 

Answer 1

Hi K, this problem can be solved in a number of ways. 

 

One solution:

 

Multiply each variable separately. In this case, you simply add the exponents of each individual variable.

 

x-term: x * x^-4 = x^1-4 = x^-3

 

y-term: y³ * y^-3 = y^3-3 = y⁰ = 1

 

z-term: z⁴ * z^-1 = z^4-1 = z³

 

Now, recombine terms noting that the y-term cancels out gives: x^-3z³. 

 

The solution cannot have negative exponents, we make x^-3 into x³ using the rule: x^-n = 1 / xⁿ.

 

Answer: z³ / x³

 

Questions?