Can someone please help explain how to do this

Question

Simplify make sure the answer has no negative exponents.

 

(x^-2z⁷) (2x²y/z^-1) 

 

 

Answer 1

(x^-2z⁷) (2x²y/z^-1)   =

 

 

 

    z⁷           2x²y

--------  •  --------     =

    x²            z^-1              ' the y/z means y is in the numerator and z in the denominator

 

 

 

z⁷ •2x²y

----------   =    ' when multiplying fractions ..... straight across....
x² z^-1

 

'in the next step we can, don't have to, commute.  Many times I like to use the commutative property to put in alphabetical order.                       

 

2x^+2-2yz⁷⁺¹   'when mult....add exponents; when div......subt.exponents: 7-(-1) = +7 = 7

 

2yz⁸               'x^+2-2 = x⁰ = 1

 

 

The reason x⁰ = 1:    

 

Example

 

 x³

----  =  1 obviously, and x^3-3 = x⁰

 x³