Question

Which of the following expressions are equivalent justify your reason

Answer 1

Rewrite the radicals using the equivalence of radicals and rational exponents.

Then check which of the expressions are equivalent.

`(A)\sqrt[4]{x^3}=x^{(3)/(4)}`
`(B)(1)/(x^(-1))=x^1=x`
`(C)\sqrt[10]{x^5\cdot x^4\cdot x^2}=\sqrt[10]{x^(5+4+2)}=\sqrt[10]{x^(11)}=x^{(11)/(10)}`
`(D)x^{(1)/(3)}\cdot x^{(1)/(3)}\cdot x^{(1)/(3)}=x^{(1)/(3)+(1)/(3)+(1)/(3)}=x^{(3)/(3)}=x^1=x`

Hence, the expressions in options B and D are equivalent.