Question

Which expression is equivalent to ((4^((5)/(4)).4^((1)/(4)))/(4^((1)/(2))))^((1)/(2))?

Answer 1

Well, this is a good practice of indices.

All of the numbers involved have the same base.

so, for the inner bracket, the powers will be (division is a minus sign for the powers):

`(5)/(4)+(1)/(4)-(1)/(2)=1`

So the inner value is

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

Answer 2

Answer: 2

Explanation:

The given expression :
`(\frac{4^{(5)/(4)}\cdot4^{(1)/(4)}}{4^{(1)/(2)}})^{(1)/(2)`

Using product rule of exponents :

`a^m\cdot a^n= a^(m+n)`

we get

`(\frac{4^{(5)/(4)}\cdot4^{(1)/(4)}}{4^{(1)/(2)}})^{(1)/(2)}\\\\=(\frac{4^{(5)/(4)+(1)/(4)}}{4^{(1)/(2)}})^{(1)/(2)}\\\\=(\frac{4^{(5+1)/(4)}}{4^{(1)/(2)}})^{(1)/(2)}\\`

`=(\frac{4^{(3)/(2)}}{4^{(1)/(2)}})^{(1)/(2)}`

Using division rule of exponents :

`(a^m)/(a^n) =a^(m-n)`

`(\frac{4^{(3)/(2)}}{4^{(1)/(2)}})^{(1)/(2)}=(4^{(3)/(2)-(1)/(2)})^{(1)/(2)}\\\\=(4^{(3-1)/(2)})^{(1)/(2)}\\\\=(4^{(2)/(2)})^{(1)/(2)}\\\\=(4^1})^{(1)/(2)}=(2* 2)^{(1)/(2)}= (2^2)^{(1)/(2)}=2`

Hence, the correct answer
`(\frac{4^{(5)/(4)}\cdot4^{(1)/(4)}}{4^{(1)/(2)}})^{(1)/(2)= 2`