*16 raised to the power of 1.5 is equal to the square root of 16, which is 4, raised to the power of 1.5. This simplifies to 4^1.5, resulting in the value of approximately 8.*

Here’s a table showing the evaluation of 16 raised to the power of 1.5:

Base (16) | Exponent (1.5) | Result |
---|---|---|

16 | 1.5 | 8 |

In this table, we’ve calculated that 16 raised to the power of 1.5 is equal to 8. This means that the square root of 16, when raised to the power of 1.5, results in 8.

**Understanding Exponents and Powers:**

Exponents are mathematical expressions that indicate how many times a number should be multiplied by itself. They are a fundamental concept in mathematics and play a crucial role in various fields, including science, engineering, and finance.

When we talk about “16 with the power of 1.5,” we are essentially calculating the square root of 16 and then raising the result to the power of 1.5.

**Step 1: Calculating the Square Root of 16**

The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, we are calculating the square root of 16, which is 4.

**Step 2: Raising the Result to the Power of 1.5**

Now that we have found the square root of 16, which is 4, we need to raise this value to the power of 1.5.

**Calculating 4^1.5:**

To raise 4 to the power of 1.5, we can break it down into two steps:

- First, raise 4 to the power of 1: 4^1 = 4
- Next, take the square root of the result: √4 = 2

**So, 4^1.5 is equal to 2.**

Now, let’s explore the significance of this result and its applications in various fields:

**Applications of Exponents and Powers:**

**Scientific Notation:**Exponents are used in scientific notation to represent very large or very small numbers compactly. For instance, the speed of light, which is approximately 299,792,458 meters per second, can be expressed as 2.9979 x 10^8 m/s.**Compound Interest:**Exponents are fundamental in finance, particularly in calculating compound interest. The compound interest formula involves raising (1 + interest rate) to the power of the number of compounding periods.**Engineering:**Engineers use exponents when working with measurements, conversions, and calculations related to electrical circuits, structural analysis, and more.**Physics:**In physics, exponents appear in equations describing various phenomena, such as the laws of motion, thermodynamics, and quantum mechanics.**Biology:**In biology, exponential growth and decay models are used to describe population growth, decay of substances, and the spread of diseases.**Computer Science:**Exponents are important in computer science, especially in algorithms and data structures, where they can be used to optimize calculations and storage.**Statistics:**Exponents are used in statistical analysis to transform data and calculate probabilities, particularly in distributions like the normal distribution.

**Conclusion:**

Understanding exponents and powers is essential in mathematics and has a wide range of applications in science, engineering, finance, and various other fields. In the case of “16 with the power of 1.5,” we found that it is equal to 2, demonstrating how exponents can simplify complex mathematical expressions. The ability to work with exponents is a valuable skill that empowers individuals to solve a multitude of problems and make sense of the world around us.

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