Problem Solving

Max@Math Revolution wrote:9^9 - 9^2 is approximation of which of the following?

A. 9^7
B. 9^8
C. 9^9
D. 9^11
E. 9^10

This is a case of relative sizes.
9^9 is a VERY BIG number (10^9 = 1,000,000,000 so 9^9 is very big also)
In comparison to 9^9, we can see that 9^2 (81) is negligible.

So, 9^9 - 9^2 is still VERY CLOSE to 9^9
Answer: C

Another way to look at it:
9^9 - 9^2 = 9^2(9^7 - 1) [notice that 9^7 - 1 is very close to 9^7]
≈ 9^2(9^7)
≈ 9^9
Answer: C

Cheers,
Brent

Max@Math Revolution wrote:9^9 - 9^2 is approximation of which of the following?

A. 9^7
B. 9^8
C. 9^9
D. 9^11
E. 9^10

We can simplify the given expression:

9^9 - 9^2

9^2(9^7 - 1)

Since 9^7 - 1 is almost the same as 9^7, we have:

9^2 x 9^7 = 9^9.

Answer: C