(Math)Simplifying using the laws of exponents
posted by ameme .
I need help with a few problems.
1.) (x^3/4 times y^1/3)^2/3
How is the answer x^1/2y^2/9
2.)(x^1/3 times y) (x^1/2 times y^4/3)
How is the answer x^1/6 over y^1/3
3.)(4a^2b^7/2)^1/2
How is the answer 2a over b^3/4
4.) (x^2/3y^1/3 over 8x^1/2y)^1/3
How is the answer x^1/18 over 2y^4/9
5.)(50x^3/4y/2x^1/2)+(x^1/2y^1/2/9x^3/4y^3/2)^1/2
How is the answer 8x^1/8y^1/2
Please help explain so I can understand. Thank you!

multiply: add exponents
raise to power: multiply exponents
(x^3/4 y^1/3)^2/3
= x^(3/4*2/3) y^(1/3*2/3)
= x^1/2 y^2/9
(x^1/3 y)(x^1/2 y^4/3)
= x^(1/3 + 1/2) y^(1  4/3)
= x^1/6 y^1/3
= x^1/6 / y^1/3
(4a^2 b^7/2)^1/2
= 4^1/2 a^(2*1/2) b^(7/2*1/2)
= 2a b^(7/4)
= 2a / b^7/4
Given answer is wrong
(x^2/3 y^1/3 / 8x^1/2 y)^1/3
= (x^(2/3  1/2) y^(1/3  1) / 8)^1/3
= x^1/18 / 2y^4/9
Just keep track of the details, and make sure your arithmetic is as good as your algebra!