Final answer:
To rewrite x - 5/7 in radical form, recognize that division can be expressed as a negative exponent and rewrite the expression as x × 7^-1, which translates to x multiplied by the 7th root of 7.
Step-by-step explanation:
To rewrite the expression x − 5 /7 in radical form, you should first recognize that dividing by a number is the same as multiplying by that number's negative exponent. Applying this idea, we can write the expression as x × 7−1. Since we are dealing with an expression where the number is raised to the power of a fraction, we can use radicals.
For instance, using the property that x2 = √ x because squaring the square root of x yields x, we can express exponents as roots. Therefore, x1/2 is the square root of x, and in general xa/b is the bth root of x raised to the ath power.
Following this logic, x × 7−1 can be written in radical form as x × 1/ √[7], since 7−1 = 1 / 71 = 1 / √[7], where √[7] represents the 7th root of the number.