3√10^4x is equivalent to -√10 3/4^x and -4√10^3x they are all equivalent
Answer:
[tex]\Rightarrow -\sqrt[8]{10^{3x}}[/tex]
D is correct
Step-by-step explanation:
Given: [tex]-(\sqrt{10^{3/4}})^x[/tex]
It is complex radical equation.
As we know,
[tex]\sqrt[n]{a}=a^{1/n}[/tex]
or viceversa
[tex]a^{1/n}=\sqrt[n]{a}[/tex]
In the given expression
[tex]\Rightarrow -(\sqrt{10^{3/4}})^x[/tex]
[tex]\Rightarrow -10^{\frac{1}{2}\cdot\frac{3}{4}\cdot x}[/tex]
simplifying the exponent
[tex]\Rightarrow -10^{\frac{3x}{8}}[/tex]
Here, the radical is 8 and change exponent to radical form
[tex]\Rightarrow -\sqrt[8]{10^{3x}}[/tex]
Hence, [tex]-(\sqrt{10^{3/4}})^x[/tex] is equivalent to [tex]\Rightarrow -\sqrt[8]{10^{3x}}[/tex]
