### Home > PC > Chapter 8 > Lesson 8.2.3 > Problem 8-108

8-108.

^{4}. He decided to use the binomial expansion by rewriting the expression as (1 + 0.1)^{4}. Use the binomial formula to expand (1 + 0.1)^{4}. Use your result to find the exact value of 1.1^{4}. (Recall that 0.1^{2} = 0.01, 0.1^{3} = 0.001) Homework Help ✎

= (1 + 0.1)^{4} = 1^{4} + 4(1)^{3}(0.1) + 6(1^{2})(0.1^{2}) + (4)(1)(0.1^{3}) + 0.1^{4}

= 1 + (4)(0.1) + (6)(0.01) + (4)(0.001) + 0.0001

= 1 + 0.4 + 0.06 + 0.004 + 0.0001

= 1.4641