simplify in radical form (x^-2/5)^1/4
Using the method of completin the square solve x2-27x+50
(x^-2/5)^1/4
keep the base, multiply the exponents
= x^(-2/20)
= x^(-1/10) or 1/x^(1/10)
To simplify the expression (x^(-2/5))^(1/4) in radical form, we can use the properties of exponents.
Step 1: Combine the exponents
When we raise a power to another power, we need to multiply the exponents. In this case, we have (x^(-2/5)) raised to the power of 1/4. Multiplying the exponents gives us (-2/5) * (1/4) = -2/20.
Step 2: Simplify the exponent
Now, we need to simplify -2/20. Since both -2 and 20 are divisible by 2, we can simplify it further: -2/20 = -1/10.
Step 3: Write the expression in radical form
Having the simplified exponent of -1/10, we can express it in radical form. A negative exponent represents taking the reciprocal of the base, so x^(-1/10) is equivalent to 1/(x^(1/10)).
Therefore, the simplified expression in radical form is 1/(x^(1/10)), where the 1/10th root of x is taken.