Simplify fourth root of x^8

Problem

√(4,x8)

Solution

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

√(4,x8)=(x8)1/4

2. Apply the power of a power rule, which states that (am)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.

x2

Final Answer

√(4,x8)=x2

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