Question

Which is equivalent to start root $10$ end root superscript three-fourths $x$ ?

Answer 1

Find the expression Root $10$ superscript three-fourths $x$ is equal to:

Consider the given data as,

The expression root $10$ superscript three-fourths $x$ this can be expressed as,

root $10$ can be expressed as $\sqrt{10}$

three-fourths $x$ can be expressed as $\frac{3}{4}x$

So, root $10$ superscript three-fourths $x$ is ${\left(\sqrt{10}\right)}^{\frac{3}{4}x}$

Let,

$$\begin{gathered} y={\left(\sqrt{10}\right)}^{\frac{3}{4}x} \\ y={\left({10}^{\frac{1}{2}}\right)}^{\frac{3}{4}x} \\ y={\left(10\right)}^{\frac{3}{8}x} \end{gathered}$$

Hence, the expression is equivalent to ${10}^{\frac{3}{8}x}$.