Question

Evaluate each expression. $$ 27^{\frac{2}{3}} $$

   Evaluate each expression.
$$
27^{\frac{2}{3}}
$$

Algebra 2

Holliday, Luchin,… 1st Edition

Chapter 7, Problem 7

Instant Answer

Solved by Expert Chris Tvrdy

03/07/2020

Step 1

This is because when you raise a power to a power, you multiply the exponents, and $\frac{1}{3} \times 2 = \frac{2}{3}$. Show more…

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Evaluate each expression. $$ 27^{\frac{2}{3}} $$

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Key Concepts

Exponentiation Laws

Exponentiation laws govern the operations involving exponents, including rules for multiplying and dividing powers with the same base, as well as raising a power to another power. These laws allow simplification and evaluation of expressions with fractional or integer exponents by providing systematic methods for combining and reducing powers.

Radical Notation

Radical notation expresses roots of numbers, such as square roots or cube roots, and is directly related to fractional exponents. Understanding that a^(1/n) is the same as the n-th root of a helps in transitioning between exponent form and radical form, which is essential for simplifying many mathematical expressions.

Fractional Exponents

Fractional exponents represent both an exponentiation and a root. For an expression a^(m/n), it means taking the n-th root of a and then raising the result to the m-th power, or equivalently, raising a to the m-th power first and then taking the n-th root. This concept bridges the operations of exponentiation and radical extraction.

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