Question

Which is equivalent toStartRoot 10 EndRoot Superscript three-fourths x ?

Answer 1

Answer:

The expression is equivalent to $10^{\frac{3}{8}x}$  

Step-by-step explanation:

Given : Expression Root 10 Superscript three-fourths x.

To find : Which is equivalent to expression ?

Solution :

The expression Root 10 Superscript three-fourths x is written as

Root 10 - $\sqrt{10}$

Three-fourths x - $\frac{3}{4}x$

So, Root 10 Superscript three-fourths x is $(\sqrt{10})^{\frac{3}{4}x}$

Let  $y=(\sqrt{10})^{\frac{3}{4}x}$

$y=(10^{\frac{1}{2}})^{\frac{3}{4}x}$

$y=10^{\frac{3}{8}x}$

The expression is equivalent to $10^{\frac{3}{8}x}$

Answer 2

Answer:

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

Step-by-step explanation:

The given expression is

$(\sqrt{10})^{\frac{3}{4}x}$

We need to find the expression which is equivalent to the given expression.

Using the property of radical expression the given expression can be rewritten as

$(10^{\frac{1}{2})^{\frac{3}{4}x}$          $[\because \sqrt{x}=x^{\frac{1}{2}}]$

Using the property of exponent, we get

$10^{\frac{1}{2}\times \frac{3}{4}x}$          $[\because (a^m)^n=a^{mn}]$

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

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