Question

10.........................

Answer 1

Hello!

The answer is:

a.
`a^{(3)/(2)}bc^(2)`

Why?

To simplify the expression, we need to transform the radical into a exponential form, then apply the exponential property.

Transforming radical to exponential form:

`\sqrt[n]{x}=x^{(1)/(n)}\\√(x)=x^{(1)/(2) }`

Power of a power property:

`(a^(m))^(n)=a^(mn)\\\\(a^(m))^{(1)/(n)}=a^{(m)/(n)}`

So,

`\sqrt[4]{a^(6)b^(4)c^(8)}=(a^(6)b^(4)c^(8))^{(1)/(4)}\\\\(a^(6)b^(4)c^(8))^{(1)/(4)}=a^{(6)/(4)}b^{(4)/(4)}c^{(8)/(4)}\\\\a^{(6)/(4)}b^{(4)/(4)}c^{(8)/(4)}=a^{(3)/(2)}bc^(2)`

Have a nice day!