Compare 4 exponent 9 and 9 exponent 4. Write 4 exponent 9 in different base

Let's compare \(4^9\) and \(9^4\):

1. **Calculating \(4^9\):**

\[
4^9 = 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 = 262144
\]

2. **Calculating \(9^4\):**

\[
9^4 = 9 \times 9 \times 9 \times 9 = 6561
\]

**Comparison:**  
\(4^9 = 262144\)  
\(9^4 = 6561\)  

Clearly, \(4^9\) is much larger than \(9^4\).

### Expressing \(4^9\) in Different Bases

Let's express \(4^9\) in a different base, say base 2:

Since \(4 = 2^2\), we can write \(4^9\) as:

\[
4^9 = (2^2)^9 = 2^{18}
\]

So, \(4^9\) can be written as \(2^{18}\) in base 2.

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Would you like more details or have any questions?

Here are 5 related questions:
1. What is \(3^7\) and how does it compare to \(7^3\)?
2. How do you convert a number from base 10 to base 5?
3. Can you express \(8^6\) in base 2?
4. What is the value of \(16^{\frac{1}{4}}\) and how is it related to powers of 2?
5. How can you simplify expressions involving exponents with different bases?

**Tip:** When comparing powers, the base and the exponent both play crucial roles in determining the magnitude of the number.

Compare 4 exponent 9 and 9 exponent 4. Write 4 exponent 9 in different base.

This article compares the powers 4^9 and 9^4, showing that 4^9 is much larger. It also explains how to express 4^9 in a different base, demonstrating that 4^9 equals 2^18 when expressed in base 2. This content is suitable for students in Grades 8-10.

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