Simplify eighth root of 6561x^4

Problem

the eighth root of 6561 x to the fourth power

Solution

1. Rewrite the radical expression using a fractional exponent.

the eighth root of 6561 x to the fourth power equals open paren 6561 x to the fourth power close paren raised to the exponent one eighth end exponent

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

6561 equals 3 to the eighth power

3. Substitute the power back into the expression.

open paren 3 to the eighth power x to the fourth power close paren raised to the exponent one eighth end exponent

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

3 to the eighth power raised to the exponent one eighth end exponent times x to the fourth power raised to the exponent one eighth end exponent

5. Simplify the exponents by performing the multiplication.

3 raised to the 8 times one eighth power times x raised to the 4 times one eighth power

3 to the first power times x raised to the one half power

6. Convert the fractional exponent back into radical form.

3 the square root of x

Final Answer

the eighth root of 6561 x to the fourth power equals 3 the square root of x

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