Simplifying Radical Expressions with Variables (1.6.2)

Question 1

Radical Expression

Answer 1

A radical expression can be written as a power with a rational exponent, where the radicand (expression within the radical symbol) is the base of the power and the reciprocal of the index of the radical is the exponent. For example, the square root of x can be written as x^1/2

Question 2

Power of a Power Property

Answer 2

The power of a power property states that a power of a power can be written as a single power with the same base where the exponents are multiplied. (a^m)n=a^mn

Question 3

Product of Powers Property

Answer 3

The product of powers property states that the product of two powers with like bases can be written as a single power with the same bases where the exponents are added. (a^m)(a^n)=a^(m+n).

Question 4

Power of a Product Property

Answer 4

The power of a product property states that the product of two or more powers with the same exponent can be written as a single power with the same exponent where the base is the product of the bases. (a^m)(b^m)=(ab)^m.
This property also works for radicals expressions with the same index (i.e., products of radical expressions where each radical is a square root, where each radical is a cube root…).