Question

Answer true or false. $\frac{1}{\left(\frac{2}{3}\right)^{-3}}=\frac{8}{27}$

Name: Problem 7, Chapter 5: Intermediate Algebra
Uploaded: 2022-03-07T03:00:04-08:00
Duration: 1 min 57 s
Channel: Rebecca Balaskovits
Description: Answer true or false. (1)/(((2)/(3))^-3)=(8)/(27)

   Answer true or false.
$\frac{1}{\left(\frac{2}{3}\right)^{-3}}=\frac{8}{27}$

Intermediate Algebra

Jerome E. Kaufmann,… 10th Edition

Chapter 5, Problem 7

Instant Answer

Solved by Expert Rebecca Balaskovits

03/07/2022

Step 1

We can use the rule of negative exponents which states that $x^{-n} = \frac{1}{x^n}$. So, we can rewrite the expression as $1 \div \left(\frac{1}{\left(\frac{2}{3}\right)^3}\right)$. Show more…

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Answer true or false. $\frac{1}{\left(\frac{2}{3}\right)^{-3}}=\frac{8}{27}$

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Key Concepts

Exponentiation of Fractions

Raising a fraction to an exponent involves applying the exponent to both the numerator and the denominator independently. This concept is fundamental in algebra as it transforms the manipulation of fractional bases into a task of separately exponentiating integers or variables, leading to simplified or more workable forms.

Reciprocals

The concept of reciprocals involves flipping the numerator and denominator of a fraction. This operation is particularly important when dealing with negative exponents or complex fractional expressions, as it allows a straightforward method to invert an expression and simplify calculations.

Negative Exponents

Negative exponents indicate that the base is to be taken as its reciprocal raised to the corresponding positive exponent. This rule simplifies expressions by converting a negative power into the inverse of a positive power, which is essential for evaluating and simplifying algebraic expressions.

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