Answer:
10. [tex]\sqrt[]{x^3}[/tex]
11. [tex]\sqrt[3]{x^5}[/tex]
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:
[tex]a^\frac{z}{n} = \sqrt[n]{a^z}[/tex]
looking at [tex]x^\frac{3}{2}[/tex], we can convert it to a radical using the formula, in which x = a, z = 3 and n = 2, we have the following:
[tex]\sqrt[]{x^3}[/tex] < 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 [tex]\sqrt[3]{x^5}[/tex], our values are: a = x, z = 5 and n = 3. we can write it as:
[tex]\sqrt[3]{x^5}[/tex]
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)
