Answer:
[tex]\frac{(5x)^{-4}}{(1x)^{-9}}[/tex] is simplified to [tex]\frac{x^5}{625}[/tex]
Step-by-step explanation:
Consider the given expression "5x to the -4 power Over 1x to the -9 power".
We can write this mathematically as,
5x to the -4 power as [tex](5x)^{-4}[/tex]
and 1x to the -9 power as [tex](1x)^{-9}[/tex]
Thus, 5x to the -4 power Over 1x to the -9 power can be written as, [tex]\frac{(5x)^{-4}}{(1x)^{-9}}[/tex]
We have to simplify the above expression,
Consider, [tex]\frac{(5x)^{-4}}{(1x)^{-9}}[/tex]
This can be re-written as,
[tex]\Rightarrow \frac{(5x)^{-4}}{(1x)^{-9}}=\frac{(5x)^{-4}}{x^{-9}}[/tex]
Solving further,
[tex]\Rightarrow \frac{(5x)^{-4}}{x^{-9}}=\frac{5^{-4}\cdot x^{-4}}{x^{-9}}[/tex],
using property of exponent,[tex]\frac{a^x}{a^y}=a^{x-y}[/tex]
[tex]\Rightarrow \frac{5^{-4}\cdot x^{-4}}{x^{-9}}=5^{-4}x^{-4-(-9)}[/tex],
[tex]\Rightarrow 5^{-4}x^{-4-(-9)}=5^{-4}x^{5}[/tex],
using property of exponent, [tex]a^{-x}=\frac{1}{a^x}[/tex]
[tex]\Rightarrow 5^{-4}x^{5}=\frac{x^5}{5^4}[/tex],
[tex]\Rightarrow \frac{x^5}{5^4}=\frac{x^5}{625}[/tex]
Thus, [tex]\frac{(5x)^{-4}}{(1x)^{-9}}[/tex] is simplified to [tex]\frac{x^5}{625}[/tex]
