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What root of x does the expression (x^3/8)^2/3 yield?

square root
cube root
fourth root
eighth root

2 Answers

3 votes
The rule for exponents of exponents is:

a^b^c=a^(b*c), in this case:

x^(3/8)^(2/3)

x^((3/8)*(2/3))

x^(6/24)

x^(1/4)

So x^(1/4) is equal to the fourth root.
User Pandu
by
7.7k points
4 votes

Answer:

Fourth root.

Explanation:

The given expression is :
(x^{(3)/(8) })^{(2)/(3) }

The power rule for exponents states that powers are multiplied


(a^(m))^(n) =a^(mn)

Applying the rule we have:


(a^{(3)/(8) }) ^{(2)/(3) } =a^{(3)/(8) .(2)/(3) } =a^{(1)/(4) }

So the x root of the expression will represent the fourth root.

User Erdna
by
7.6k points

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