Answer:
A 4x^2 y^3 (x^2 y)^1/3
Step-by-step explanation:
(8x^4 y^5) ^ (2/3)
Separate into pieces because (abc) ^d = a^d b^d c^d
8 ^2/3 x^4^2/3 y ^ 5 ^2/3
Replace 8 with 2^3
2^3 ^2/3 x^4^2/3 y ^ 5 ^2/3
We know that a^b^c = a^ (b*c)
2 ^(3*2/3) x ^ (4*2/3) y ^ (5*2/3)
2^2 x^(8/3) y ^ (10/3)
4 x^(8/3) y ^ (10/3)
Take out the whole numbers out of the exponents
4 x ^ 2 x^2/3 y ^ 3 y ^ 1/3
4x^2 y^3 x^2/3 y^1/3
Now we take out the 1/3 by (a^c b^c) = (ab)^c
4x^2 y^3 (x^2 y)^1/3
