Answer:
12. 7xy ∛(xy^2)
13. 3x^2|y| sqrt(7x)
14. 5 x^4 y ^4 y ∛(y^2)
Explanation:
12. (343 x^4y^5) ^ 1/3
separate
343^1/3 x^4 ^ 1/3 y^5 ^ 1/3
using the power of power we can multiply the powers
343 ^ 1/3 x^ 4/3 y ^ 5/3
simplify
7 x^ 4/3 y ^ 5/3
if the power is greater than 1 we can split it
7 x x^ 1/3 y y ^ 2/3
7xy ( xy^2 ) ^ 1/3
7xy ∛(xy^2)
13. (189 x^5y^6)^ 1/2/(3y^4)^ 1/2
combine
( (189 x^5y^6)/(3y^4))^ 1/2
(189/3 * x^5 * y^6/y^4) ^ 1/2
when we divide exponents with the same base, we subtract the exponent
(63 * x^5 * y^2) ^ 1/2
split
63 ^ 1/2 x^ 5 ^ 1/2 y ^ 2 ^ 1/2
sqrt (63) * sqrt * (x^5) * sqrt(y^2)
sqrt(9*7) sqrt( x^4 *x) * sqrt(y^2)
sqrt(9) * sqrt(7) sqrt(x^4) sqrt(x) sqrt(y^2)
we need to make sure to take the positive value of sqrt(y^2)
3sqrt(7) x^2 sqrt(x) | y|
3x^2|y| sqrt(7x)
14. (625 x^17 y^16) ^1/3 / (5 x^5 y^2) ^ 1/3
combine
(625 x^17 y^16 / 5 x^5 y^2) ^ 1/3
(625/5 * x^17/x^5 * y^16/y^2) ^ 1/3
when we divide exponents with the same base, we subtract the exponent
(125 x^(17-5) y^(16-2)) ^ 1/3
(125 x^12 y ^ 14) ^ 1/3
split
125 ^ 1/3 x^ 12 ^ 1/3 y^ 14 ^ 1/3
power to the power ( multiply the power)
125 ^ 1/3 x^ 4 y ^ 14/3
5 x^4 y ^ 14/3
if the power is greater than 1 we can split it
5 x^4 y ^4 y ^2/3
5 x^4 y ^4 y ∛(y^2)