Question

Write each of the following expressions as a power of 2: 4⁻⁶ ⋅ 4⁴ ⋅ (2³ ⋅ 2⁻⁴ )⁻¹?

Answer 1

To write each of the expressions as a power of 2, we can simplify and combine the powers of 2 to get the final result of 1/8.

Step-by-step explanation:

To write each of the expressions as a power of 2, we can use the fact that 4 can be written as 2^2. Let's break down each expression:

4^(-6) = (2^2)^(-6) = 2^(2*(-6)) = 2^(-12)

4^4 = (2^2)^4 = 2^(2*4) = 2^8

(2^3 * 2^(-4))^(-1) = (2^(3+(-4)))^(-1) = (2^(-1))^(-1) = 2^1 = 2

Now we can combine the powers of 2:

2^(-12) * 2^8 * 2 = 2^(-12+8+1) = 2^(-3) = 1/8