How do you simplify (2x^2y^4)^3/2?

Question

I am trying to do an algebra review quiz for a Calculus I class.

Sincerely,  D. McClure

Answer 1

3, 5 and 8 have no common factors so their LCM is 3×5×8=120.

We need a 4-digit number, so let's find the smallest. 1000/120=8⅓. So the next highest integer is 9.

9×120=1080 is the smallest 4-digit number which is divisible by 120, therefore it's the smallest 4-digit number that 3, 5 and 8 all divide into. But there are many more we can find by adding 120 as many times as we like until just before we get the first 5-digit number. We can actually find 75 4-digit numbers divisible by 3, 5 and 8 (1080=9×120 up to 9960=83×120).