Question

Which is equivalent to -√10 3/4^x?

Answer 1

Answer:

$\Rightarrow -\sqrt[8]{10^{3x}}$

D is correct

Step-by-step 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

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

$\Rightarrow -10^{\frac{1}{2}\cdot\frac{3}{4}\cdot x}$

simplifying the exponent

$\Rightarrow -10^{\frac{3x}{8}}$

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 $\Rightarrow -\sqrt[8]{10^{3x}}$

Answer 2

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