Question

What is the value of y in the product of powers below? 8 cubed times 8 Superscript negative 5 Baseline times 8 Superscript negative 2 Baseline = StartFraction 1 Over 8 squared EndFraction

Answer 1

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.

Explanation:

Answer 2

Answer:
`y=0`

Explanation:

The complete exercise is attached.

For this exercise it is important to remember:

1. The Product of powers property. This property states that:

`(a^m)(a^n)=a^((m+n))`

2. The multiplication of signs:

`(+)(+)=+\\(-)(-)=+\\(-)(+)=-\\(+)(-)=-`

Then, given:

`8^3*8^(-5)*8^y=8^(-2)=(1)/(8^2)`

You can identify that
`8^(-2)` is obtained by applying the Product of powers property:

`8^(3+(-5)+y)=8^(-2)=(1)/(8^2)`

Based on the explained above, you can write the following equation:

`3+(-5)+y=-2`

Therefore you must solve for the variable "y" in order to find its value. You get that this is:

`3-5+y=-2\\\\-2+y=-2\\\\y=-2+2\\\\y=0`