https://file.aiquickdraw.com/mathbot/file/17266702627057emazq0x.jpg

The problem asks to find \( (64)^{\frac{3}{8}} \).

Let's solve this step by step:

### Step 1: Express 64 as a power of 2
Since \( 64 = 2^6 \), we can rewrite the expression as:
\[
(64)^{\frac{3}{8}} = (2^6)^{\frac{3}{8}}
\]

### Step 2: Apply the exponentiation rule
Using the rule \( (a^m)^n = a^{m \cdot n} \), we multiply the exponents:
\[
(2^6)^{\frac{3}{8}} = 2^{6 \cdot \frac{3}{8}} = 2^{\frac{18}{8}} = 2^{\frac{9}{4}}
\]

### Step 3: Simplify the exponent
Now we have \( 2^{\frac{9}{4}} \), which can be rewritten as:
\[
2^{\frac{9}{4}} = \left( 2^2 \right)^{\frac{9}{4}} = \sqrt[4]{512}
\]

Thus, \( (64)^{\frac{3}{8}} \approx 5.7 \) when evaluated numerically.

Would you like more details on any step or have any questions?

Here are 5 related questions to explore:
1. How would you simplify \( (27)^{\frac{2}{3}} \)?
2. What is the value of \( (16)^{\frac{3}{4}} \)?
3. How do you express \( 125^{\frac{2}{3}} \) in terms of powers of 5?
4. What is the general rule for calculating fractional exponents?
5. How do you compute \( (81)^{\frac{3}{4}} \)?

**Tip:** Fractional exponents represent roots and powers. For instance, \( a^{\frac{m}{n}} \) means the \( n \)-th root of \( a^m \).

Learn how to solve the fractional exponent (64)^(3/8) by breaking it down step by step. Understand the relationship between exponents and radicals, and follow the laws of exponents to simplify powers.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation