1.6.2 Simplifying Radical Expressions with Variables

Question 1

A radical expression

Answer 1

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

The product of powers property

Answer 2

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 3

The power of a power property

Answer 3

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 4

The power of a product property

Answer 4

• 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…)