Question

Which expression is equivalent to

Answer 1

x^2/3

option B is the right option

solution,

`( {x}^{ (4)/(3) } . {x}^{ (2)/(3) }) ^{ (1)/(3) } \\ = ({x ^{ (4)/(3) + (2)/(3) } )}^{ (1)/(3) } \\ = ({x}^{ (4 + 2)/(3) } ) ^{ (1)/(3) } \\ = ( {x}^{ (6)/(3) } ) ^{ (1)/(3) } \\ = {x}^{ (6 * 1)/(3 * 3) } \\ = {x}^{ (6)/(9) } \\ divide \: 6 \: and \: 9 \: by \: 3 \\ = {x}^{ (2)/(3) }`

hope this helps...

Good luck on your assignment...

Answer 2

the expression is equivalent to x^2/3

Explanation:

[x^4/3 x^2/3]^1/3

=[x^4/3+(2/3)]^1/3

by using laws of exponent

a^m a^n=a^m+n

=[x^4/3+2/3]^1/3

=[x^6/3]^1/3

={x^2]^1/3

by using law of exponent

(a^m)^n=a^mn

=x^2×1/3

=x^2/3

i hope this will help you :)