Respuesta :
Answer:
The expression is equivalent to [tex]10^{\frac{3}{8}x}[/tex]
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 - [tex]\sqrt{10}[/tex]
Three-fourths x - [tex]\frac{3}{4}x[/tex]
So, Root 10 Superscript three-fourths x is [tex](\sqrt{10})^{\frac{3}{4}x}[/tex]
Let [tex]y=(\sqrt{10})^{\frac{3}{4}x}[/tex]
[tex]y=(10^{\frac{1}{2}})^{\frac{3}{4}x}[/tex]
[tex]y=10^{\frac{3}{8}x}[/tex]
The expression is equivalent to [tex]10^{\frac{3}{8}x}[/tex]
Answer:
[tex]10^{\frac{3}{8}x}[/tex]
Step-by-step explanation:
The given expression is
[tex](\sqrt{10})^{\frac{3}{4}x}[/tex]
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
[tex](10^{\frac{1}{2})^{\frac{3}{4}x}[/tex] [tex][\because \sqrt{x}=x^{\frac{1}{2}}][/tex]
Using the property of exponent, we get
[tex]10^{\frac{1}{2}\times \frac{3}{4}x}[/tex] [tex][\because (a^m)^n=a^{mn}][/tex]
[tex]10^{\frac{3}{8}x}[/tex]
Therefore, the expression [tex]10^{\frac{3}{8}x}[/tex] is equivalent to the given expression.
