We know that there are (4^9)^5 ⋅ 4^0 at the library, so we just need to simplify this to get the answer.
(4^9)^5 ⋅ 4^0
=(4^9)^5×1
=(4^9)^5
=4^9×5
=4^45. As a result, the total number of books at the library is 4^45 books at the library or B is the final answer. Hope it help!

6 0

2 years ago

Using binomial theorem, expand (x+6)^8 edit: You could use the help of combinations too.

Pavlova-9 [17]

x⁸ + 48x⁷ + 1008x⁶ + 12096x⁵ + 90720x⁴ + 435456x³ + 1306368x² + 2239488x + 1679616

Explanation:

We know

(x+y)ⁿ = ∑ ⁿCₐxⁿ⁻ᵃyᵃ

and ⁿCₐ = n! / ( a! ) . ( n-a )!

So,

(x+6)⁸ = ⁸C₀x⁸ + ⁸C₁(x)⁸⁻¹(6)¹ + ⁸C₂(x)⁸⁻²(6)² + ⁸C₃(x)⁸⁻³(6)³ + .......+ ⁸C₈(x)⁸⁻⁸(6)⁸

= ₓ⁸ + 8x⁷ₓ 6 + 28x⁶ₓ 36 + 56x⁵ₓ 216 + 70x⁴ₓ 1296 + 56x³ₓ 7776 + 28x²ₓ 46656 + 8x . 279936 + 1679616

= x⁸ + 48x⁷ + 1008x⁶ + 12096x⁵ + 90720x⁴ + 435456x³ + 1306368x² + 2239488x + 1679616

Thus, the expansion of ( x+6)⁸ using binomial theorm is

x⁸ + 48x⁷ + 1008x⁶ + 12096x⁵ + 90720x⁴ + 435456x³ + 1306368x² + 2239488x + 1679616

4 0

2 years ago