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:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

step-by-step explanation: the answer for wha if rt is 10 centimeters long, and wha is st? it’s 6