express the third root of(8a^3y^5) using rational exponents.
Please show your work!
(8a^3y^5)^1/3
8^1/3 a^3^1/3 y^5^1/3
2 a y^5/3
thank you
To express the third root of (8a^3y^5) using rational exponents, we need to rewrite the expression in exponential form.
Step 1: Rewrite 8 as a power of a number that has a perfect cube root.
8 can be written as 2^3.
Step 2: Rewrite a^3 as (a^3)^(1/3).
Taking the cube root of a^3 gives us (a^3)^(1/3).
Step 3: Rewrite y^5 as (y^5)^(1/3).
Taking the cube root of y^5 gives us (y^5)^(1/3).
Now, let's put all the parts together.
The expression (8a^3y^5)^(1/3) can be simplified as:
(2^3 * (a^3)^(1/3) * (y^5)^(1/3)).
Using the rule of exponents, we can move the exponents outside the parentheses:
2^(3/3) * (a^(3/3)) * (y^(5/3)).
Simplifying further, we have:
2 * a * (y^(5/3)).
Therefore, the third root of (8a^3y^5) can be expressed using rational exponents as 2 * a * (y^(5/3)).