Final answer:
The value of n in the equation 4³×8²/2n=2⁴ is 8.
Step-by-step explanation:
To find the value of n in the equation 4³×8²/2n=2⁴, we can simplify the expression step by step. First, let's calculate the values of the exponents: 4³ = 4 × 4 × 4 = 64 and 8² = 8 × 8 = 64. Next, we can rewrite the equation as (64 × 64) / 2n = 16. Simplifying further, we get 4096 / 2n = 16. To isolate n, we can cross-multiply and solve for n: 4096 = 16 × 2n. Dividing both sides by 16, we have 256 = 2n. Finally, we can find the value of n by taking the logarithm base 2 of both sides: log2 (256) = log2 (2n). Since log2 (256) = 8, we get 8 = n.