Algebra 2: Simplifying Radicals with Exponents 8^(2/3) * 9^(1/2) - Evaluate

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SUMMARY

The discussion focuses on evaluating the expression 8^(2/3) * 9^(1/2) by applying the properties of exponents. Participants highlight the formula a^(m/n) = √[n]{a^m} as a critical concept for simplifying radicals. The specific evaluations discussed include 8^(2/3) and 9^(1/2), leading to the conclusion that 8^(2/3) simplifies to 4 and 9^(1/2) simplifies to 3. Therefore, the final result of the multiplication is 4 * 3 = 12.

PREREQUISITES
  • Understanding of exponent rules and properties
  • Familiarity with radical expressions
  • Basic algebraic manipulation skills
  • Knowledge of square roots and cube roots
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  • Study the properties of exponents in depth
  • Learn how to simplify complex radical expressions
  • Explore additional examples of multiplying numbers with exponents
  • Practice solving problems involving fractional exponents
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Students studying algebra, educators teaching exponent rules, and anyone looking to improve their skills in simplifying radical expressions.

woahitzyou
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8^2/3 (9^1/2) <---- times (multiply)

evaluate.
THANKSS
 
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So what do you know about multiplying numbers with exponents?
 
woahitzyou said:
8^2/3 (9^1/2) <---- times (multiply)

evaluate.
THANKSS
One thing youshould know is that:
[tex]a ^ {\frac{m}{n}} = \sqrt[n] {a ^ m}[/tex]
For example:
[tex]25 ^ {\frac{1}{2}} = \sqrt{25} = 5[/tex]
[tex]5 ^ {\frac{3}{2}} = \sqrt{5 ^ 3} = \sqrt{125}[/tex].
Now what's:
[tex]8 ^ {\frac{2}{3}} \quad \mbox{and} \quad 9 ^ {\frac{1}{2}}[/tex]?
Can you go from here? :)
 

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