Question

Which is equivalent to -√10^3/4x?

Answer 1

I know you have choices so I'm hoping this is one of them.
The way you write the problem is really important for us to help you. I'm still not quite sure about where the x is in the problem. I'm thinking it is multiplied at the end. Sooooo here goes.
- sqrt (10) ^ (3/4) x
sqrt 10 is the same as 10 ^ (1/2)
- (10)^(1/2)^(3/4) x
multiply (1/2) and (3/4)
-(10)^(3/8) x
- eighth root(10^3) x

Answer 2

`-\sqrt[8]{10^(3x) }`

Explanation:

Using fractional exponent rule:

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

In this case:

`a=10\\x=(3)/(4)x\\ y=2`

Hence:

`-\sqrt{10^{(3)/(4)x } } =-10^{(3x)/((4)/(2) ) }`

To divide fractions, you can use this fact:

`(a)/(b) /(c)/(d) =(a*d)/(b*c)`

So:

`(3x)/(4) / (2)/(1) =(3x*1)/(4*2) =(3x)/(8)`

Therefore:

`-\sqrt{10^{(3)/(4)x } } =-10^{(3x)/(8) } =--\sqrt[8]{10^(3x) }`