Question

How can the properties of rational exponents be applied to simplify expressions with radicals or rational exponents?

Answer 1

@Hero

Answer 2

A rational exponent that i found is \[\sqrt[7]{4z}\]

Answer 3

1.you can translate radicals into their rational exponent
2. you can combine rational exponents by finding their common denominator
3.you can in general simplify the expression if you the properties

Answer 4

that expression is equal to (4z)^1/7 do you get that?

Answer 5

so for the answer i would write


The Properties can be applied because you can translate radicals into their rational exponent. This equation \[\sqrt[7]{4z}\] is equivalent to \[4z^\frac{ 1 }{ 7 }\]

Answer 6

thats just an example but no. for the answer you could say with the properties of rational exponents you have the ability to further evaluate rational exponents through addition, subtraction, multiplication, and division

Answer 7

i guess im not sure what she is looking for specifically

Answer 8

like for division if you are given \[\sqrt{27}/\sqrt{3} \]
it might seem like there isnt much you can do to simplify right?

Answer 9

but by using the properties of radicals you know that expression is equivalent to \[\sqrt{27/3}\] now if you divide whats inside the radical you get 9

Answer 10

now whats the sqrt(9)?

Answer 11

so by these properties we took sqrt(27)/sqrt(3) and evaluated it to get 3

Answer 12

3

Answer 13

good

Answer 14

thats just one example of radical properties, there are like 5 more but thats the one for divison

Answer 15

i dont think shes asking you to write them all out so my response should work in theory but i dont know your teacher

Answer 16

With the properties of rational exponents you have the ability to further evaluate rational exponents through addition, subtraction, multiplication, and division so taking the equation √(27/3) divide them and you get 9 then evaluate Sqrt of 9 and you get 3 which is the answer.

Answer 17

So this would work for the answer thx