Expand (1+a)^5 use your expansion to estimate (0.8)^5 correct to four decimal places?

To expand (1+a)^5, we can use the binomial theorem:

(1+a)^5 = 1 + 5a + 10a^2 + 10a^3 + 5a^4 + a^5

Now, let's estimate (0.8)^5 using this expansion:

(0.8)^5 ≈ 1 + 5(0.8) + 10(0.8)^2 + 10(0.8)^3 + 5(0.8)^4 + (0.8)^5

Calculating this expression:

(0.8)^5 ≈ 1 + 4 + 6.4 + 5.12 + 2.048 + 0.32768

(0.8)^5 ≈ 18.89768

Therefore, (0.8)^5 is approximately 18.8977 when rounded to four decimal places.

0.3277