Answer:
y = - 8
Step-by-step explanation:
Using the rule of exponents
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]
Note that 8 = 2³ and 16 = [tex]2^{4}[/tex]
Given
[tex]8^{y}[/tex] = [tex]16^{y+2}[/tex], then
[tex](2^3)^{y}[/tex] = [tex](2^4)^{y+2}[/tex]
[tex]2^{3y}[/tex] = [tex]2^{4(y+2)}[/tex]
Since the bases on both sides are equal, both 2 then equate the exponents
4(y + 2) = 3y
4y + 8 = 3y ( subtract 3y from both sides )
y + 8 = 0 ( subtract 8 from both sides )
y = - 8
