84. use properties of exponents to rewrite each expression with only positive, rational exponents. then find the numerical value of each expression when x = 9, y= 8, and z= 16. in each case, the expression evaluates to a rational number.
c. x-3/2 y4/3 z-3/4

a) 1/27

b) 16

c) 1/8

Step-by-step explanation:

a)

One of the properties of the exponents tells us that when we have a negative exponent we can express it in terms of its positive exponent by turning it into the denominator (and changing its sign), so we would have:

And now, solving for x = 9 we have:

b)

This is already a positive rational exponent so we are just going to substitute the value of y = 8 into the expression

c)

Using the same property we used in a) we have:

And now, solving for z = 16 we have: