Simplify eighth root of 6561x^4

Problem

√(8,6561*x4)

Solution

1. Rewrite the radical expression using a fractional exponent.

√(8,6561*x4)=(6561*x4)1/8

2. Factor the constant 6561 into its prime base to simplify the power.

6561=3

3. Substitute the power back into the expression.

(3*x4)1/8

4. Apply the power of a product rule by multiplying the exponents.

(3)1/8⋅(x4)1/8

5. Simplify the exponents by performing the multiplication.

3(8⋅1/8)⋅x(4⋅1/8)

3⋅x1/2

6. Convert the fractional exponent back into radical form.

3√(,x)

Final Answer

√(8,6561*x4)=3√(,x)

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