Question

Write each expression without the radical.

open the picture.

Answer 1

Part 1)
`4m^{(1)/(2)}`

Part 2)
`3(r)^{(1)/(3)}(s)^{(2)/(3)}(t)^{(4)/(3)}`

Part 3)
`3(x)^{(9)/(4)}`

Explanation:

Part 1) Write each expression without the radical.

we have

`√(16m)`

we know that

`16=4^2`

substitute

`√(4^2m)`

Remember that

`\sqrt[a]{x^b}=x^{(b)/(a)}`

`(x^a)^(b)=x^(ab)`

so

`√(4^2m)=(4^2m)^{(1)/(2)}=(4^2)^{(1)/(2)}(m)^{(1)/(2)}=4m^{(1)/(2)}`

Part 2) Write each expression without the radical.

we have

`\sqrt[3]{27rs^2t^4}`

we know that

`27=3^3`

substitute

`\sqrt[3]{3^3rs^2t^4}`

Remember that

`\sqrt[a]{x^b}=x^{(b)/(a)}`

`(x^a)^(b)=x^(ab)`

so

`\sqrt[3]{3^3rs^2t^4}=(3^3rs^2t^4)^{(1)/(3)}=(3^3)^{(1)/(3)}(r)^{(1)/(3)}(s^2)^{(1)/(3)}(t^4)^{(1)/(3)}=3(r)^{(1)/(3)}(s)^{(2)/(3)}(t)^{(4)/(3)}`

Part 3) Write each expression without the radical.

we have

`\sqrt[4]{81x^9}`

we know that

`81=3^4`

substitute

`\sqrt[4]{3^4x^9}`

Remember that

`\sqrt[a]{x^b}=x^{(b)/(a)}`

`(x^a)^(b)=x^(ab)`

so

`\sqrt[4]{3^4x^9}=(3^4x^9)^{(1)/(4)}=(3^4)^{(1)/(4)}(x^9)^{(1)/(4)}=3(x)^{(9)/(4)}`