Simplify the given expression to radical form, justify each step by identifying the properties of rational exponents used. All work must be shown.
x to the two–thirds power, over x to the four–ninths power

Question

Simplify the given expression to radical form, justify each step by identifying the properties of rational exponents used. All work must be shown.
x to the two–thirds power, over x to the four–ninths power

anonymous · Answer

@kawaiicat123

anonymous · Answer

First you simplify. Rule of exponents: when dividing you can subtract the exponents if they have the same base. So that gets you to x to the 2/9 power(2/3-4/9=2/9). When you have a fraction as an exponent the top number becomes what you multiply by and the bottom number becomes the root. So in this case the answer would be 2 times the 9th root of x.