Simplify ( fourth root of 16x)^3

Problem

(√(4,16*x))3

Solution

1. Apply the power of a product rule to the expression inside the radical.

√(4,16*x)=√(4,16)⋅√(4,x)

2. Evaluate the fourth root of the constant coefficient.

√(4,16)=2

3. Rewrite the expression using the simplified coefficient.

(√(4,16*x))3=(2√(4,x))3

4. Distribute the exponent of 3 to both factors inside the parentheses.

(2√(4,x))3=2⋅(√(4,x))3

5. Simplify the constant and rewrite the radical using a fractional exponent.

2=8

(√(4,x))3=x3/4

6. Combine the terms into the final simplified form.

8*x3/4=8√(4,x3)

Final Answer

(√(4,16*x))3=8√(4,x3)

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