How would you simplify (2x^2)^3 over 5 times 15x^-2 over 2x^3?

Question

I used ^ to show to the _ power. i.e: 2x^3= 2x cubed

Answer 1

(2x^2)^3 over 5 times 15x^-2 over 2x^3

Remember that x^-2 = 1/x^2. Thus, 15x^-2 / 2x^3 = 15 / (x^2 * 2x^3) = 15 / 2x^5

(2x^2)^3 = 8x^6.

So:
8x^6 / 5 * 15 / 2x^5 = 120 x^6 / 10 x^5

120/10 = 12
x^6 / x^5 = x

so the answer is 12x.