Question

Which is equivalent to

16 Superscript three-fourths x ?
Rootindex 4 StartRoot 16 EndRoot Superscript 3x
Rootlndex 4 x StartRoot 16 EndRoot cubed
3 Rootindex 3 StartRoot 16 End Root Superscript 4 x
E
Rootindex 3 x StartRoot 16 End Root Superscript 4

Answer 1

A)
`16^(3)/(4)=\sqrt[4]{16^3}`

Explanation:

1) According to Exponents Law, whenever we have a number raised to a fraction this is the same as having a root of its number whose index is the denominator, raised to the numerator.

`n^{(a)/(b)}=\sqrt[b]{n^(a)}\\16^{(3)/(4)}=\sqrt[4]{16^(3)}=\sqrt[4]{4096}=\sqrt[4]{2^(12)}=8`

Then
`16^(3)/(4)=\sqrt[4]{16^3}`