Question

Which is equivalent to 64 Superscript one-fourth?

2 RootIndex 4 StartRoot 4 EndRoot

4

16

16 RootIndex 4 StartRoot 4 EndRoot

Answer 1

2 RootIndex 4 StartRoot 4 EndRoot

Explanation:

we have

`64^{(1)/(4)}`

Decompose the number 64 in prime factors

`64=2^(6)=2^(4)2^(2)`

substitute

`64^{(1)/(4)}=(2^(4)2^(2))^{(1)/(4)}=2^{(4)/(4)}2^{(2)/(4)}=2\sqrt[4]{4}`

Answer 2

Option 1 -
`64^{(1)/(4)}=2\sqrt[4]{4}`

Explanation:

Given : Expression 64 Superscript one-fourth i.e.
`64^{(1)/(4)}`

To find : Which is equivalent to expression ?

Solution :

Step 1 - Write the expression,

`64^{(1)/(4)}`

Step 2 - Factor the term 64,

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

`=(2^6)^{(1)/(4)}`

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

Step 3 - Apply exponent rule,
`(x^a)^{(1)/(b)}=x^{(a)/(b)}`

`=(2)^{(4)/(4)}\cdot (2)^{(2)/(4)}`

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

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

`=2\sqrt[4]{4}`

Therefore,
`64^{(1)/(4)}=2\sqrt[4]{4}`

So, Option 1 is correct.