Simplify the given expression to radical form and 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 and 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

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.

aum · Answer

$\Large \frac {x^m}{x^n} = x^{m-n}$

aum · Answer

$\Large \frac {x^{2/3}}{x^{4/9}} = x^{2/3-4/9} = x^?$

anonymous · Answer

So it would be 2 times the 9th root of x?

aum · Answer

9th root of x^2 or simply x raised to 2/9.
$\Large x^{2/9} = \sqrt[9]{x^2}$

anonymous · Answer

Ohhh ok

anonymous · Answer

So is that the answer?

aum · Answer

Yes.  I'd probably leave it as $\Large x^{2/9}$ because the exponents in the original problem are all given as fractions.

anonymous · Answer

Ok thanks