Given:
Consider the equation is
[tex]\dfrac{h^{16}}{h^x}=\dfrac{1}{h^{24}}[/tex]
To find:
The value of x.
Solution:
We have,
[tex]\dfrac{h^{-16}}{h^x}=\dfrac{1}{h^{24}}[/tex]
Using properties of exponents, we get
[tex]h^{-16-x}=h^{-24}[/tex] [tex][\because \dfrac{a^m}{a^n}=a^{m-n},a^{-n}=\dfrac{1}{a^n}][/tex]
On comparing both sides, we get
[tex]-16-x=-24[/tex]
Add 16 on both sides.
[tex]-x=-24+16[/tex]
[tex]-x=-8[/tex]
Multiply both sides by -1.
[tex]x=8[/tex]
Therefore, the value of x is 8.
