Question

stage 10
the number of circles at stage 10 is extremely large.
write an expression to represent this number.

stage	number of circles (kiran)	number of circles (jada)	number of circles (noah)
2	4	2·2	$2^2$
3	8	2·2·2	$2^3$
4	16	2·2·2·2	$2^4$
5	32	2×2×2×2×2	$2^5$
...	...	...	...
10	1024	2×2×2×2×2×2×2×2×2×2	$2^{10}$

Explanation:

Step1: Observe the pattern

From the table, we can see that the number of circles for each stage follows a pattern where the number of circles is \(2\) raised to the power of the stage number.

Step2: Apply the pattern to stage 10

For stage \(n\), the number of circles is \(2^n\). When \(n = 10\), the expression for the number of circles is \(2^{10}\).

Answer:

\(2^{10}\)