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
One of your friends sends you an email asking you to explain how all of the following expressions have the same answer.
the cube root of x cubed

:x to the one–third power • :x to the one–third power • x to the one–third power

1 over x to the –1 power

the eleventh root of the quantity of x to the fifth times x to the fourth times x squared

Answer 1

\[\frac{ x ^{\frac{ 2 }{ 3 }} }{ x ^{\frac{ 4 }{ 9 }} }=x ^{\frac{ 2 }{ 3 }}*x ^{-\frac{ 4 }{ 9 }}=x ^{\frac{ 2 }{ 3 }-\frac{ 4 }{ 9 }}\]