Question

Write as a radical and then simplify. $(-64) 1 / 3$

   Write as a radical and then simplify.
$(-64) 1 / 3$

Elementary Algebra

Elementary Algebra

John Redden 1st Edition

Chapter 8, Problem 36

Instant Answer

Solved by Expert Sherrie Fenner

02/04/2022

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This is represented as $\sqrt[3]{-64}$. Show more…

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Write as a radical and then simplify. $(-64) 1 / 3$

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Key Concepts

Rational Exponents

Rational exponents are a way to denote roots and powers using fractions. The numerator represents the power, while the denominator indicates the root to be taken. This concept allows expressions involving roots and exponents to be manipulated algebraically using the laws of exponents.

Radical Notation

Radical notation provides another method to express roots. Instead of using a fractional exponent, the n-th root is written with a radical sign, where n indicates the degree of the root. This representation is especially useful for visualizing and simplifying expressions involving roots.

Cube Roots and Simplification

Cube roots are specific radical expressions where the degree is three, meaning you are finding a number that, when raised to the third power, returns the original value. A key aspect is that cube roots can be taken of negative numbers, yielding negative results. Simplification involves expressing the radical in its simplest form by extracting perfect cube factors.

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