Final answer:
The expression 16⁵/⁴×16¹/⁴/(16¹/²)² simplifies to 2 by combining multiplication and division of powers and applying the rules of exponents.
Step-by-step explanation:
The expression to evaluate is 16⁵/⁴×16¹/⁴/(16¹/²)². This involves rules of exponents where we multiply and divide powers of the same base by adding and subtracting their exponents, respectively.
First, let's combine the multiplication part of the expression:
- 16⁵/⁴×16¹/⁴ = 16⁵/⁴+¹/⁴ = 16⁶/⁴
Next, let's simplify the division part of the expression:
Now we can divide the two results:
- 16⁶/⁴ / 16¹ = 16⁶/⁴-¹ = 16ⁱ/⁴
The final simplified expression is 16ⁱ/⁴, which is equal to 2. In other words, the base 16 is raised to the power of 1.5 and the square root of 16 is 4, therefore the result is 4 raised to the power of 1.5.