Thank you for the clarification! The expression you provided is:

\[
\frac{2^{18}}{\left(\frac{2^6}{2^3}\right)^2}
\]

Let's simplify this step by step.

### Step-by-Step Solution

1. **Simplify the expression inside the parentheses**:

\[
\frac{2^6}{2^3}
\]

Using the rules of exponents, specifically \(\frac{a^m}{a^n} = a^{m-n}\), we have:

\[
\frac{2^6}{2^3} = 2^{6-3} = 2^3
\]

2. **Square the result of the expression inside the parentheses**:

\[
\left(2^3\right)^2
\]

Using the rule \((a^m)^n = a^{m \cdot n}\), we get:

\[
(2^3)^2 = 2^{3 \cdot 2} = 2^6
\]

3. **Simplify the entire expression**:

Now, substitute back into the original expression:

\[
\frac{2^{18}}{2^6}
\]

Again, using the rule \(\frac{a^m}{a^n} = a^{m-n}\), we have:

\[
\frac{2^{18}}{2^6} = 2^{18-6} = 2^{12}
\]

### Final Answer

The simplified form of the expression is:

\[
2^{12}
\]

And calculating the value:

\[
2^{12} = 4096
\]

So, the final result is:

\[
4096
\]

Would you like more details or have any questions? 

Here are some related questions to explore further:

1. How do you apply exponent rules to simplify expressions?
2. What are some common mistakes when working with exponents?
3. How can exponents be used in real-world applications?
4. What are logarithms, and how do they relate to exponents?
5. How can understanding exponents help in solving exponential equations?

**Tip:** Always apply exponent rules carefully, especially when dealing with fractions or negative exponents, to ensure accuracy.

Learn how to simplify the expression 2^18 / ((2^6) / (2^3))^2 step-by-step. This problem involves applying exponent rules, specifically the rules for fractions and exponents. Suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation