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Chapter 0: Problem 100

Simplify the expressions. $$ 2^{1 / 3} 2^{-1} 2^{2 / 3} 2^{-1 / 3} $$

Short Answer

Expert verified
The short version of the answer is: \(2^{\frac{-1}{3}}\).

Step by step solution

01

Write out the expression

Given the expression: \( 2^{1 / 3} \cdot 2^{-1} \cdot 2^{2 / 3} \cdot 2^{-1 / 3} \)
02

Use laws of exponent

Recall that when multiplying numbers with the same base and different exponents, we add the exponents. Using this rule, we can simplify the given expression: \(2^{\frac{1}{3}} \cdot 2^{-1} \cdot 2^{\frac{2}{3}} \cdot 2^{-\frac{1}{3}} = 2^{\frac{1}{3} - 1 + \frac{2}{3} - \frac{1}{3}}\)
03

Simplify exponents

Now, we can simplify the expression by combining the exponents: \(2^{\frac{1}{3} - 1 + \frac{2}{3} - \frac{1}{3}} = 2^{\frac{1 - 3 + 2 - 1}{3}}\)
04

Calculate the final exponent

Simplify the exponent: \(2^{\frac{1 - 3 + 2 - 1}{3}} = 2^{\frac{-1}{3}}\)
05

Write the final solution

The simplified expression is: \(2^{\frac{-1}{3}}\)

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Most popular questions from this chapter

By any method, determine all possible real solutions of each equation Check your answers by substitution. \(2 x^{2}-x-3=0\)

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