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What is the index (root) of the radical expression that is equivalent to (9^3/5)^5/18?

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User Ndsc
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The index (root) of a radical expression refers to the number that indicates the degree of the root. In the given expression, (9^(3/5))^(5/18), we have a nested radical.

To simplify the expression, we can apply the exponent rules. When we raise a power to another power, we multiply the exponents:

(9^(3/5))^(5/18) = 9^((3/5)*(5/18))

Multiplying the exponents, we get:

9^((3/5)*(5/18)) = 9^(15/90)

Simplifying the exponent further, we have:

9^(15/90) = 9^(1/6)

Therefore, the index (root) of the equivalent radical expression is 6.
User Howy
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