Question

perform the operation and simplify completely show all work. properties of expoenents/ super helpful property.

Answer 1

The rule of multiplication of the exponents is

`a^m.a^n=a^(m+n)`

We will use this rule with our question

`x^{(5)/(9)}.x^{(2)/(3)}`

We must add the fractions 5/9 and 2/3

To add fractions they must have the same denominators

Since the lowest common factor of 9 and 3 is 9, then

`(5)/(9)+(2)/(3)=(5)/(9)+(2*3)/(3*3)=(5)/(9)+(6)/(9)=(11)/(9)`

Then the expression is

`x^{(5)/(9)}.x^{(2)/(3)}=x^{(5)/(9)+(2)/(3)}=x^{(11)/(9)}`