Answer:
10. ![\sqrt[]{x^3}](https://tex.z-dn.net/?f=%5Csqrt%5B%5D%7Bx%5E3%7D)
11. ![\sqrt[3]{x^5}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%5E5%7D)
12.
a. the sum of 2 rational numbers: is always a rational number. (ex: 2 + 2 = 4)
b. the sum of an irrational and a rational number: is not rational (ex: 1/3 + π)
c. the product of 2 rational numbers: is a rational number (ex: 45/2 × 4/7 = 90/7)
d. the product of an irrational and a rational number: not rational (ex: 4/5 × π)
Step-by-step explanation:
10. to write an exponent in radical form, we can use the following formula:
![a^\frac{z}{n} = \sqrt[n]{a^z}](https://tex.z-dn.net/?f=a%5E%5Cfrac%7Bz%7D%7Bn%7D%20%3D%20%5Csqrt%5Bn%5D%7Ba%5Ez%7D)
looking at 
, we can convert it to a radical using the formula, in which x = a, z = 3 and n = 2, we have the following:
< we did not write 2 because 2 is the square root symbol with no need to write a 2
11. using the same formula as above, we can convert the radical into exponential form
in , our values are: a = x, z = 5 and n = 3. we can write it as:
12.
a. the sum of 2 rational numbers: is always a rational number. (ex: 2 + 2 = 4)
b. the sum of an irrational and a rational number: is not rational (ex: 1/3 + π)
c. the product of 2 rational numbers: is a rational number (ex: 45/2 × 4/7 = 90/7)
d. the product of an irrational and a rational number: not rational (ex: 4/5 × π)
