Answer:
[tex]\frac{5\sqrt{x}}{x^4}[/tex]
Step-by-step explanation:
The given expression is
[tex]\frac{5}{\sqrt{x^7}}[/tex]
We need to find the simplified form of the given expression.
Using product property of exponent we get,
[tex]\frac{5}{\sqrt{x^6\cdot x}}[/tex] [tex][\because a^ma^n=a^{m+n}][/tex]
[tex]\frac{5}{\sqrt{x^6}\cdot \sqrt{x}}[/tex] (Distributive property)
[tex]\frac{5}{\sqrt{(x^3)^2}\cdot \sqrt{x}}[/tex] [tex][\because (a^m)^n=a^{mn}][/tex]
[tex]\frac{5}{x^3\cdot \sqrt{x}}[/tex]
Multiply numerator and denominator by [tex]\sqrt{x}[/tex] to rationalize denominators.
[tex]\frac{5}{x^3\cdot \sqrt{x}}\times \frac{\sqrt{x}}{\sqrt{x}}[/tex]
[tex]\frac{5\sqrt{x}}{x^3\cdot (\sqrt{x})^2}[/tex]
[tex]\frac{5\sqrt{x}}{x^3\cdot x}[/tex]
[tex]\frac{5\sqrt{x}}{x^4}[/tex]
Therefore, the simplified form of given expression is [tex]\frac{5\sqrt{x}}{x^4}[/tex].
