To solve the expression \( 9.8^{5/2} \), we follow these steps:

### Step 1: Calculate the exponent
The exponent \( \frac{5}{2} \) can be interpreted as \( 9.8^2.5 \). This means we need to first square 9.8 and then take the square root of that result, followed by raising it to the power of 5.

### Step 2: Calculate \( 9.8^{2.5} \)
\[ 9.8^{2.5} = 9.8^{5/2} \]

Calculating \( 9.8^{2.5} \):
\[ 9.8^{2.5} \approx 902.427 \]

So, the value of \( 9.8^{5/2} \approx 902.427 \).

### Final Answer:
\[ \boxed{902.427} \]

Would you like more details on any part of the solution?

Here are some related questions to explore further:
1. What is \( 9.8^2 \)?
2. How do you simplify expressions with fractional exponents?
3. What is the general formula for \( a^{m/n} \)?
4. How do you convert a fractional exponent to a radical expression?
5. What is \( 9.8^{0.5} \)?
6. What is \( 9.8^{3} \)?
7. What is the result of \( 9.8^{-5/2} \)?
8. How does changing the base affect the result of an expression?

**Tip:** Fractional exponents can be rewritten as roots, which can sometimes make calculations easier. For example, \( a^{m/n} = \sqrt[n]{a^m} \).

Learn how to calculate 9.8 raised to the power of 5/2 with a step-by-step solution. Understand the concept of fractional exponents and exponentiation rules. Suitable for advanced high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation