SAT Question

[Math Tutor]

If [tex]2x-3y=3[/tex], then find [tex]\frac{16^x}{64^y}=?[/tex]

[red12dog34]

Spoiler: show

Solution
[tex]2x-3y=3\Rightarrow y=\displaystyle\frac{2x-3}{3}[/tex]
Then [tex]\displaystyle\frac{16^x}{64^y}=\displaystyle\frac{16^x}{64^{\frac{2x-3}{3}}}=\frac{16^x}{\left(64^{\frac{1}{3}}\right)^{2x-3}}=\frac{4^{2x}}{4^{2x-3}}=4^3=64[/tex]

[Guest]

16= 2^4 so 16^x= 2^(4x)333
64= 2^6 so 64^y= 2^(6y)

16^x/64^x= 2^(4x)/2^(6y)= 2^(4x- 6y)= 2^(2(2x- 3y)= 2^(2(3))= 2^6= 64.