Solving Complex Root Expressions for SEO

In this article, we will explore how to solve a complex algebraic expression involving roots and exponents. Understanding such expressions is essential for SEO professionals working on math-related content. By breaking down the problem step-by-step, we can enhance the readability and understanding of our content, which in turn improves SEO performance.

Expression Breakdown

The expression we are dealing with is:

sqrt[5]{frac{1}{243}} times sqrt[3]{sqrt{729}} times sqrt{sqrt[3]{frac{1}{64}}}

Breaking Down the Expression

First Term: sqrt[5]{frac{1}{243}} Second Term: sqrt[3]{sqrt{729}} Third Term: sqrt{sqrt[3]{frac{1}{64}}}

Solving the First Term

The first term of the expression is sqrt[5]{frac{1}{243}}.

Factorize 243: 243 3^5 Then, frac{1}{243} 3^{-5} Therefore, sqrt[5]{3^{-5}} 3^{-1} frac{1}{3}

Solving the Second Term

The second term of the expression is sqrt[3]{sqrt{729}}.

Factorize 729: 729 27^2 3^6 Therefore, sqrt{729} 729^{1/2} 3^3 27 Thus, sqrt[3]{27} 3

Solving the Third Term

The third term of the expression is sqrt{sqrt[3]{frac{1}{64}}}.

Factorize 64: 64 4^3 2^6 Therefore, frac{1}{64} 2^{-6} Hence, sqrt[3]{2^{-6}} 2^{-2} frac{1}{4} Then, sqrt{frac{1}{4}} frac{1}{2}

Combining the Terms

Now, we can combine all three results:

sqrt[5]{frac{1}{243}} times sqrt[3]{sqrt{729}} times sqrt{sqrt[3]{frac{1}{64}}} frac{1}{3} times 3 times frac{1}{2}

Convert each fraction to a common denominator of 6:

frac{1}{3} frac{2}{6} 3 frac{18}{6} frac{1}{2} frac{3}{6}

Add the fractions:

frac{2}{6} frac{18}{6} frac{3}{6} frac{23}{6}

Final Answer

The solution to the expression is: boxed{frac{23}{6}}.

Final Simplified Expression: sqrt[5]{frac{1}{243}} times sqrt[6]{729} times sqrt[6]{frac{1}{64}} boxed{3 frac{5}{6}}

Conclusion

By breaking down complex mathematical expressions, we can ensure that our content remains clear and understandable for SEO optimization. This approach not only enhances readability but also improves the likelihood of Google favoring our content in search results.

Related Keywords

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By focusing on these keywords and structuring the content in a clear, logical manner, we can optimize our content for better SEO performance.