Simplify the expression. a. (64 x^9)^1 / 3 b. (25 x^3 y^4)^1 / 2

Name: Problem 7, Chapter 3: Applied Mathematics: For the Managerial, Life, and Social Sciences
Uploaded: 2021-05-12T19:42:26-08:00
Duration: 1 min 52 s
Channel: Priyanka Sadarangani
Description: Simplify the expression. a. (64 x^9)^1 / 3 b. (25 x^3 y^4)^1 / 2

step 1 Okay, in this question we have to simplify the expression. In the part A expression is given 64

Simplify the expression. a. (64 x^9)^1 / 3 b. (25 x^3 y^4)^1...

Key Concepts

Power of a Product Rule

The power of a product rule states that a product raised to an exponent is equivalent to each factor raised to that exponent individually. This rule simplifies expressions by allowing each component of the product to be handled separately, which is particularly useful when dealing with variables and numerical coefficients within the same expression.

Radicals

Radicals, or root expressions, are another way to represent fractional exponents. The nth root of any expression can be written as raising that expression to the power of 1/n. This duality between radicals and rational exponents is essential for converting between the two forms and simplifying complex expressions effectively.

Exponent Laws

Understanding exponent laws, such as the power of a power and the power of a product rules, is fundamental in algebra. When raising an expression to an exponent, each factor within the product is raised to that exponent separately. This principle enables the simplification of expressions like (ax^n)^m by rewriting it as a^m * x^(n*m).

Rational Exponents

Rational exponents provide a way to express roots as fractional powers, where the numerator is the exponent and the denominator is the root. For example, an expression like x^(1/3) represents the cube root of x. This concept allows for easier manipulation of expressions involving both powers and roots, especially when simplifying or performing algebraic operations.

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