SOLUTION: (^13sqrt2x^6y)^5 rewrite with rational exponents

Question 625265: (^13sqrt2x^6y)^5 rewrite with rational exponents
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
"^13sqrt"???
Do you mean ? If yes, then

This is not a square root. It is a 13th root.
The 13 is not an exponent even though it may look like one. It is the "index" of the radical which indicates which kind of root it is.
To post problems with roots that are not square roots, do not use "sqrt" to describe it. For this problem you could either:
- Use some English like: "(the 13th root of (2x^6y))^5"; or
- Teach yourself the syntax used by algebra.com to display these mathematical expressions. Click on the "Show Source" link above to see what I typed to get the 13th root to display. Look for the expressions inside the sets of three braces: {...}

Radical expressions can be replaced with fractional/rational exponents. The fraction (or ratio) to use when replacing a radical with a rational exponent is 1 over the index of the radical. So to replace our radical with a rational exponent we will use 1/13:

Now we just use the power of a power rule for exponents (i.e. multiply the exponents:

P.S. Square roots do not have a visible index. For example: . A missing/invisible index is considered to be a 2. IOW, means the same thing as . So the rational exponent for square roots is 1/2.
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