I am kinda stuck on this one
Simplify: ^5sqrt(x^7 y^4)
I don't know what to do for this problem. I am lost with what to do with the exponents when you have a number on the outside.
To simplify the expression ^5√(x^7 y^4), you need to understand how to deal with exponents when there is a number outside the radical sign.
In this case, the number outside the radical sign is 5, which represents the index of the radical. The index tells you the power to which the expression inside the radical sign will be raised.
To simplify the expression:
Step 1: Break down the expression inside the radical sign into its prime factors.
The expression inside the radical sign is x^7 y^4. To break it down, separate the exponents of each variable into prime factors:
x^7 = x * x * x * x * x * x * x
y^4 = y * y * y * y
Step 2: Determine the power of each prime factor.
Since the index is 5, you need to find the power of each prime factor that is divisible by 5.
In the expression, x has a power of 7, which is not divisible by 5, so it remains outside the radical sign.
On the other hand, y has a power of 4, which is divisible by 5.
Step 3: Simplify.
The expression ^5√(x^7 y^4) becomes x^7 * y^(4/5).
Therefore, the simplified form of ^5√(x^7 y^4) is x^7 * y^(4/5).