Question

Express the quotient of r to the power of six sevenths divided by r to the power of two sevenths as a radical

Answer 1

See below (I hope this helps!)

Explanation:

When dividing exponents of the same base, we can simply subtract the powers so the new power would be 6 / 7 - 2 / 7 = 4 / 7, hence we need to write
`r^{(4)/(7) }` as a radical. When writing fractional exponents as radicals, the denominator of the fractional exponent is the index of the radical and the numerator is the exponent of the base inside the radical, hence, our answer is
`\sqrt[7]{r^(4) }`.