Question

simplify the cube root of
108a^16b^9

Answer 1

how many times does 3 go in to 9?

Answer 2

3

Answer 3

ok so out comes \(b^3\)

Answer 4

how many times does 3 go in to 16?

Answer 5

taking the cube root is the same as raising the base to the power 1/3
cube root of 108a^16b^9 = (108a^16b^9)^1/3
when you raise a power to a power multiply the powers
108^1*1/3 *a^(16*1/3) * b^(9*1/3)
(4*27)^1/3*a^5*a^1/3*b^3
3a^5b^3 cube root 4a

note that multiplying by 1/3 is the same as dividing by 3 so you will get the same answer as above