Question

Simplify each expression. $$ (-3)^{2}\left(r^{\frac{1}{4}}\right)^{2} $$

   Simplify each expression.
$$
(-3)^{2}\left(r^{\frac{1}{4}}\right)^{2}
$$

Algebra 1 Common Core

Algebra 1 Common Core

Randall I.… 1st Edition

Chapter 7, Problem 101

Instant Answer

Solved by Expert Lourence Gonhovi

04/01/2020

Step 1

Since any number squared is positive, $(-3)^{2}$ equals $9$. Show more…

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Simplify each expression. $$ (-3)^{2}\left(r^{\frac{1}{4}}\right)^{2} $$

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Key Concepts

Negative Bases in Exponentiation

When exponentiating a negative base, it is important to consider the parity of the exponent. If the exponent is even, the result is positive, and if it is odd, the result is negative. This concept is especially important in ensuring accurate simplification of expressions involving negative numbers raised to powers.

Rational Exponents

Rational exponents represent both exponentiation and extraction of roots. An expression with a rational exponent can be interpreted as a radical, where the numerator of the exponent indicates the power and the denominator signifies the root. Understanding this relationship is crucial when simplifying expressions that contain fractional exponents.

Exponentiation Basics

Exponentiation is a mathematical operation involving two numbers, the base and the exponent, which indicates how many times the base is multiplied by itself. It is a fundamental concept that underlies many algebraic operations and simplifications, especially when combining or manipulating terms raised to powers.

Power of a Power Rule

The power of a power rule states that when an expression with an exponent is raised to another exponent, the exponents are multiplied. This rule is essential when simplifying expressions that involve nested exponents, ensuring the expression is reduced to a simpler form that is easier to evaluate or manipulate.

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