Math Problem Statement

Solution

The image contains a math problem that appears to involve exponentiation. Let's analyze the problem statement and solve it.

Problem Statement

The problem appears to be evaluating an expression with exponents: (7879)11×810=?\left(\frac{7^8}{7^9}\right)^{11} \times 8^{10} = ?

Solution Steps

  1. Simplify the Fraction: 7879=789=71\frac{7^8}{7^9} = 7^{8-9} = 7^{-1}

  2. Apply the Exponent to the Result: (71)11=711(7^{-1})^{11} = 7^{-11}

  3. Rewrite in Terms of Multiplication: 711×8107^{-11} \times 8^{10}

  4. Evaluate if Needed: If you want to find a numerical answer or compare with options, you may proceed to use the exact powers or find an approximate value, but since the problem might be asking for the exact expression, this would be the simplified form.

Final Simplified Expression

711×8107^{-11} \times 8^{10}

To match this with the provided options (as seen faintly in the image), one would need to convert this expression to a similar format, perhaps considering factors or looking for approximate values if options are numerical.

Would you like a detailed breakdown of further steps to find a numerical value or check against options? Here are some further topics you might be interested in:

  1. How to convert the simplified expression into a standard form?
  2. How to approximate 7117^{-11} and 8108^{10}?
  3. What are some properties of exponents that are useful in simplifying such expressions?
  4. How to handle negative exponents in calculations?
  5. Understanding the significance of base numbers in exponential functions.

Tip: When working with exponentiation, always remember that multiplying like bases allows for adding exponents, and dividing allows for subtracting exponents.

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Math Problem Analysis

Mathematical Concepts

Exponentiation
Fractional Exponents
Properties of Exponents

Formulas

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Theorems

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Suitable Grade Level

High School