Answer:
x = 24
Step-by-step explanation:
using the rule of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m +n)}[/tex]
consider left side
[tex]5^{\frac{x}{6} }[/tex] × [tex]5^{\frac{x}{2} }[/tex]
= [tex]5^{\frac{x}{6} }[/tex] × [tex]5^{\frac{3x}{6} }[/tex]
= [tex]5^{\frac{4x}{6} }[/tex]
then
[tex]5^{\frac{4x}{6} }[/tex] = [tex]5^{16}[/tex]
since the bases on both sides are equal, both 5 then equate exponents
[tex]\frac{4x}{6}[/tex] = 16 ( multiply both sides by 6 )
4x = 96 ( divide both sides by 4 )
x = 24
