Answer:
[tex]-\sqrt[8]{10^{3x} }[/tex]
Step-by-step explanation:
Using fractional exponent rule:
[tex]a^{\frac{x}{y} } =\sqrt[y]{a^{x} }[/tex]
In this case:
[tex]a=10\\x=\frac{3}{4}x\\ y=2[/tex]
Hence:
[tex]-\sqrt{10^{\frac{3}{4}x } } =-10^{\frac{3x}{\frac{4}{2} } }[/tex]
To divide fractions, you can use this fact:
[tex]\frac{a}{b} \div\frac{c}{d} =\frac{a*d}{b*c}[/tex]
So:
[tex]\frac{3x}{4} \div \frac{2}{1} =\frac{3x*1}{4*2} =\frac{3x}{8}[/tex]
Therefore:
[tex]-\sqrt{10^{\frac{3}{4}x } } =-10^{\frac{3x}{8} } =--\sqrt[8]{10^{3x} }[/tex]
