Question

Which is equivalent to -√10 3/4^x?

3√10^4x

-4√10^3x

-6√10^4x

-8√10^3x

Answer 1

3√10^4x is equivalent to -√10 3/4^x and -4√10^3x they are all equivalent

Answer 2

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

D is correct

Explanation:

Given:
`-(\sqrt{10^(3/4)})^x`

It is complex radical equation.

As we know,

`\sqrt[n]{a}=a^(1/n)`

or viceversa

`a^(1/n)=\sqrt[n]{a}`

In the given expression

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

`\Rightarrow -10^{(1)/(2)\cdot(3)/(4)\cdot x}`

simplifying the exponent

`\Rightarrow -10^{(3x)/(8)}`

Here, the radical is 8 and change exponent to radical form

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

Hence,
`-(\sqrt{10^(3/4)})^x` is equivalent to
`\Rightarrow -\sqrt[8]{10^(3x)}`