Question

Evaluate each expression. $$ \left(-\frac{1}{9}\right)^{2} $$

   Evaluate each expression. 
$$
\left(-\frac{1}{9}\right)^{2}
$$

Algebra A Combined Function

Algebra A Combined Function

Elayn Martin-Gay 4th Edition

Chapter 5, Problem 10

Instant Answer

Solved by Expert Erika Bustos

02/05/2022

Step 1

The exponent of two tells us to multiply the base, $-\frac{1}{9}$, by itself. Show more…

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Evaluate each expression. $$ \left(-\frac{1}{9}\right)^{2} $$

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Key Concepts

Even Exponent and Sign Rule

When any number, whether positive or negative, is raised to an even exponent, the result is always non-negative. This occurs because multiplying an even number of negative factors results in a positive product, a key consideration when dealing with negative bases.

Operations on Fractions

When raising a fraction to a power, the exponent is applied separately to both the numerator and the denominator. This allows the fraction to be simplified by computing the power for each part individually, which is especially useful in evaluating expressions involving fractions.

Exponentiation

Exponentiation is the operation of raising a base to a certain power, which means multiplying the base by itself as many times as indicated by the exponent. This concept provides the framework for evaluating expressions where numbers are involved in repeated multiplication.

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