Question

Simplify. $$ 5 a 2 b \cdot-27 a 3 b 3------\sqrt{3} $$

   Simplify.
$$
5 a 2 b \cdot-27 a 3 b 3------\sqrt{3}
$$

Elementary Algebra

Elementary Algebra

John Redden 1st Edition

Chapter 8, Problem 56

Instant Answer

Solved by Expert James Kiss

02/02/2022

Step 1

We know that -27 can be written as -3 cubed, and a cubed b cubed can be written as (ab)^3. So, we can rewrite the expression as follows: $$ 5 a^2 b \cdot \sqrt[3]{(-3)^3 a^3 b^3} $$ Show more…

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Simplify. $$ 5 a 2 b \cdot-27 a 3 b 3------\sqrt{3} $$

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Key Concepts

Multiplication of Monomials

This concept involves multiplying algebraic terms by multiplying their numerical coefficients and applying the exponent rules for variables. When multiplying monomials, the coefficients are multiplied together while the exponents of like bases are added. This method is essential for simplifying expressions that consist of products of terms with variables.

Properties of Exponents

Understanding exponent rules is crucial when working with products of powers. The rules state that when you multiply two expressions that have the same base, you add their exponents. This property is key to simplifying terms such as a^m * a^n, which becomes a^(m+n). Mastery of these rules allows you to streamline algebraic expressions.

Multiplication Involving Negative Numbers

When multiplying terms that include negative numbers, the sign of the final product is determined by the arithmetic rules for signs. Multiplying a positive number by a negative number yields a negative product, and this must be handled carefully during simplification to ensure the overall expression maintains the correct sign.

Operations with Radicals

This concept deals with the inclusion of square roots or other radicals in algebraic expressions. When dividing by a radical or multiplying terms that include a radical, it is important to recognize how the radical interacts with the numerical coefficients and variables. Sometimes it may be necessary to rationalize the denominator or combine like terms under the radical to further simplify the expression.

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