Question

Write the symbolic expression for each of the following descriptions, then get rid of the radical and make them exponential expressions in fractional form.

11. The eighth root of fifty-seven to the sixth degree
12. The square root of Y to the fourteenth degree
13. The nth root of m to the o plus p degree.
14. The fifth root plus x of eighty-one to the third power.
15. The cube root of five squared.

Answer 1

11.
`57^(6/8)`

12.
`Y^(14/2)`

13.
`m^{(o+p)/(n)}`

14.
`81^{(3)/(50+x)}`

15.
`5^(2/3)`

Explanation:

When converting from radicals to rational exponents, there's a quick, easy rule to remember:

• 
  `\sqrt[n]{x} =\sqrt[\text{index}]{\text{radicand}}`
• the exponent is
  `\frac{\text{power}}{\text{root}}`
• 
  `\sqrt[n]{x} = x^(1/n)`

The "power" represents the exponent of the radical/radicand, while the "root" represents the index.

11. the eight root of fifty-seven to the sixth degree.

1. Write the expression in radical form:
   `\sqrt[8]{57^6}`
2. Rewrite using the exponent rule (power over root):
   `57^(6/8)`

12. the square root of Y to the fourteenth power.

1. Write the expression in radical form:
   `\sqrt[2]{Y^(14)}`
2. Rewrite using the exponent rule (power over root):
   `Y^(14/2)`

13. the nth root of m to the o plus p degree.

1. Write the expression in radical form:
   `\sqrt[n]{m^(o+p)}`
2. Rewrite using the exponent rule (power over root):
   `m^{(o+p)/(n)}`

14. The fifth root plus x of eighty-one to the third power.

1. Write the expression in radical form:
   `\sqrt[5+x]{81^(3)}`
2. Rewrite using the exponent rule (power over root):
   `81^{(3)/(50+x)}`

15. The cube root of five squared.

1. Write the expression in radical form:
   `\sqrt[3]{5^(2)}`
2. Rewrite using the exponent rule (power over root):
   `5^(2/3)`