Simplify each expression as much as possible, and rationalize denominators when applicable. 5/√x^7=?
Accepted Solution
A:
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].