Simplify the following:
(6 c d^2)^2/(24 c^5 d^4)
Multiply each exponent in 6 c d^2 by 2:
6^2 c^2 d^(2×2)/(24 c^5 d^4)
2×2 = 4:
(6^2 c^2 d^4)/(24 c^5 d^4)
(6^2 c^2 d^4)/(24 c^5 d^4) = d^4/d^4×(6^2 c^2)/(24 c^5) = (6^2 c^2)/(24 c^5):
(6^2 c^2)/(24 c^5)
Combine powers. (6^2 c^2)/(24 c^5) = (6^2 c^(2-5))/24:
(6^2 c^2-5)/24
2-5 = -3:
(6^2 c^-3)/24
6^2 = 36:
36/(24 c^3)
The gcd of 36 and 24 is 12, so 36/(c^3×24) = (12×3)/((12×2) c^3) = 12/12×3/(2 c^3) = 3/(2 c^3):
Answer: |
| 3/(2c^3)
