Question

3. Han found a way to compute complicated expressions more easily. Since 2.5 = 10,

he looks for pairings of 2s and 5s that he knows equal 10. For example,
(2.5)4 = 15 104 = 150,000. Use Han's
3.24.55= 3.24.54.5 = (3.5)
technique to compute the following:
a. 2^4 * 5 * (3*5)³
b.
2^3 *5^2*(2.3)²*(3.5)²/3^2

Answer 1

To compute 2^4 * 5 * (3*5)^3 using Han's technique, simplify the expression within the parentheses, insert the pairing of 2s and 5s that equals 10, and then multiply the numbers together.

Step-by-step explanation:

To compute the expression 2^4 * 5 * (3*5)^3 using Han's technique, we can first simplify the expression within the parentheses, (3*5)^3.

This is equivalent to (15)^3, which is 15 * 15 * 15 = 3375. Next, we insert the pairing of 2s and 5s that equals 10, which gives us 2^4 * (2.5)^3 * 5. We can simplify (2.5)^3 as (10)^3, which is 1000. So, the expression becomes 2^4 * 1000 * 5.

Finally, we can multiply the numbers together to get the result: 16,000 * 5 = 80,000.