Math Problem Statement

Divide sign in the bracket

Solution

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

218(2623)2\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:

2623\frac{2^6}{2^3}

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

2623=263=23\frac{2^6}{2^3} = 2^{6-3} = 2^3

  1. Square the result of the expression inside the parentheses:

(23)2\left(2^3\right)^2

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

(23)2=232=26(2^3)^2 = 2^{3 \cdot 2} = 2^6

  1. Simplify the entire expression:

Now, substitute back into the original expression:

21826\frac{2^{18}}{2^6}

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

21826=2186=212\frac{2^{18}}{2^6} = 2^{18-6} = 2^{12}

Final Answer

The simplified form of the expression is:

2122^{12}

And calculating the value:

212=40962^{12} = 4096

So, the final result is:

40964096

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.

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Math Problem Analysis

Mathematical Concepts

Exponents
Fractional Exponents

Formulas

Exponent rules

Theorems

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Suitable Grade Level

Grades 9-12