step 1 27 to the 2 thirds is the same thing as 3 to the 3 to the 2 thirds, which is equal to 3 to the 6

Question

Simplify. $$ 27^{2 / 3} $$

Name: Problem 5, Chapter 1: College Algebra Essentials
Uploaded: 2021-08-05T14:24:09-08:00
Duration: 20 s
Channel: James Kiss
Description: Simplify. 27^2 / 3

   Simplify.
$$
27^{2 / 3}
$$

College Algebra Essentials

Julie Miller 1st Edition

Chapter 1, Problem 5

Instant Answer

Solved by Expert James Kiss

08/05/2021

Step 1

So, 27^{2/3} becomes (3^3)^{2/3}. Show more…

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Simplify. $$ 27^{2 / 3} $$

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Key Concepts

Rational Exponents

Rational exponents represent a combination of roots and powers. An exponent expressed as a fraction, such as a/b, implies that the base is raised to the power a and then the b-th root of that result is taken. This dual nature allows one to convert between radical notation and exponentiation, making certain expressions easier to simplify or compute.

Exponentiation Rules

Exponentiation rules are essential properties in algebra that govern how to work with powers. One key rule is that raising a power to another power multiplies the exponents, which can simplify calculations involving complex expressions. These rules ensure consistency when manipulating expressions with exponents and are vital for understanding and simplifying algebraic expressions.

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