Simplify. Assume all variables are positive.

Question

1. 9⁴√8 - 2⁴√8
2. 9³√3 - ³√24
3. √81x⁸y⁶
4. ⁴√16x¹²/y²⁰
5. √n + 9√n

Answer 1

Here are the rules you need to know in order to be able to answer the questions.

1. Use the fourth root of 8 as if it's a variable. How would you answer 9a-2a?
2. The third root of 24 is the third root of 8 times the third root of 3. You can figure the 3rd root of 8 as 2 (2 x 2 x 2 =8). So you can pull out a 2 and have 2 times the third root of 3 for your second number.
3. Take the square root of each piece. What times itself gives you 81? What times itself gives you x⁸? (Remember that you add the exponents when you multiply, so x⁴ times x⁴ gives you x⁸). What times itself gives you y⁶?
4. The fourth root of x¹² is the number that can be multiplied by itself 4 times to get to x¹². Hint: x³ times x³ is x⁶.
5. See number 1.