not sure how to phrase the questions. planning to start school in fall after 20 years. trying to prepare.thanx

Question

1.m to the sixth power. please find the root.
2.cube root of 5b to the nineth - use product rule to simplify
3. 9/144 root
4. 32 inside the root box with small 4 to the outside left of the root.--use product rule to simplify. thanks

Answer 1

1.m to the sixth power. please find the root.
= m^6
root basically means sqrt (m^6)
= (m^6)^(1/2)
=m^3

2.cube root of 5b to the nineth - use product rule to simplify
(5b)^9
cube rt (5b)^9
= [(5b)^9]^(1/3)
=(5b)^3

3. 9/144 root
sqrt(9/144)
= sqrt 9 / sqrt 144
= sqrt (3^2) / sqrt (12^2)
= 3/12

4. 32 inside the root box with small 4 to the outside left of the root.--use product rule to simplify. thanks
32 = 2^5
32 inside the root box with small 4 to the outside left of the root means fourth root
= (2^5)^(1/4)
= 2^(5/4) = 2 (2)^(1/4)

Answer 2

Taking the square root is the same as raising something to the power of 1/2. Cube root is the same as raising it to the power of 1/3, etc.

So, for #1,
sqrt(m^6) is the same as (m^6)^(1/2). To simplify, multiply the exponents (6*1/2). So, the answer is m^3.

#2
cube rt ((5b)^9) = ((5b)^9)^(1/3) = (5b)^3

NOTE: If the question is cube root of 5 (b^9), then the answer is 5^1/3 b^3.

#3
Square root of 9 is 3 (3*3 = 9)
Square root of 144 is 12 (12*12 = 144)
So the square root of 9/144 is 3/12.

3/12 reduces to 1/4.

#4
Fourth root of 32 = Fourth root of 16*2

The fourth root of 16 is 2 (2*2*2*2 = 16), so the 2 is written outside the root box, and the other two stays inside. So the answer is 2 * 4th root of 2 (i.e. 2*(2 inside the root box with small 4 to the outside left of the root)).

Hope that helps! Good luck to you =)

Answer 3

First thing you do is use quasi-math notation.

1. Like m^6. I assume by the "root", you want the SQUARE root, which is sqrt[m^6] or m^3.
3. Here you want sqrt(9/144). Since both numbers are squares of integers, their roots can be obtained as 3/12 or 1/4
4, Here you want the 4th root of 32 or 32^(1/4).
This is (16*2)^(1/4). Then you wind up with
2 * 2^(1/4)

Answer 4

u can do it