Answer: [tex]y=0[/tex]
Step-by-step explanation:
For this exercise it is important to remember:
1. The Product of powers property. This property states that:
[tex](a^m)(a^n)=a^{(m+n)}[/tex]
2. The multiplication of signs:
[tex](+)(+)=+\\(-)(-)=+\\(-)(+)=-\\(+)(-)=-[/tex]
Then, given:
[tex]8^3*8^{-5}*8^y=8^{-2}=\frac{1}{8^2}[/tex]
You can identify that [tex]8^{-2}[/tex] is obtained by applying the Product of powers property:
[tex]8^{3+(-5)+y}=8^{-2}=\frac{1}{8^2}[/tex]
Based on the explained above, you can write the following equation:
[tex]3+(-5)+y=-2[/tex]
Therefore you must solve for the variable "y" in order to find its value. You get that this is:
[tex]3-5+y=-2\\\\-2+y=-2\\\\y=-2+2\\\\y=0[/tex]
Answer:
You're trying to find the value of y that would result in 8^-2. When you multiply terms with the same base, you can add the exponents. 3+-5=-2 and -2-(-2) equals 0, so therefore y is equal to 0.
Step-by-step explanation:
