Simplify fourth root of x^8

Problem

√(4,x^8)

Solution

1. Identify the radical expression and rewrite it using a fractional exponent. The rule for converting radicals to exponents is √(n,a^m)=a^m/n

√(4,x^8)=(x^8)^1/4

2. Apply the power of a power rule, which states that (a^m)^n=a^(m⋅n) Multiply the exponents together.

x^(8⋅1/4)

3. Simplify the resulting exponent by performing the multiplication.

8⋅1/4=2

4. Write the final simplified expression.

x^2

Final Answer

√(4,x^8)=x^2

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