Question

9. Consider the expression

x'y'
a. Without simplifying, evaluate the expression for x = 5 and y = 7. (You may get some big numbers.)
b. Rewrite the expression using the laws of exponents.
c. Evaluate the expression you wrote in part b with the same values: x = 5 and y = 7.
d. Did you get same value for parts a and c? Why?

Answer 1

Answer: 270

Step-by-step explanation: a. When x = 5 and y = 7,

x'y' = 5'7'

= 10110101 (in binary)

= 181 (in decimal)

b. x'y' can be written as (2^3+1)(2^2+1)(2^1+1)(2^0+1), where ^ denotes exponentiation.

c. When x = 5 and y = 7,

x'y' = (2^3+1)(2^2+1)(2^1+1)(2^0+1)

= (8+1)(4+1)(2+1)(1+1)

= 953*2

= 270

d. No, we did not get the same value for parts a and c. The reason for this is that in part a, we evaluated x'y' using binary arithmetic, while in part c, we evaluated it using decimal arithmetic. The two methods of arithmetic yield different results.