Question

80. Use properties of exponents to rewrite each expression as either an integer or as a quotient of integers p/q to show the expression is a rational number.

c. 16*3/2*(1/27)2/3

Answer 1

This expression can be rewritten as 24/9

Explanation:

c)
`16(3/2)(1/27^(2/3) )`

`16(3/2) (1/27^(2/3))= 16(3)/(2) ((1)/(27^(2/3) ))=(48)/(2)((1)/(27^(2/3) ))=(24)/(27^(2/3) ) =(24)/(9)`

Thus, since this expression is a quotient of two integers 24 and 9, it is a rational number.