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

Answer: $y=0$

Step-by-step 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:

$8^3*8^{-5}*8^y=8^{-2}=\frac{1}{8^2}$

You can identify that $8^{-2}$ is obtained by applying the Product of powers property:

$8^{3+(-5)+y}=8^{-2}=\frac{1}{8^2}$

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:

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

Answer 2

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: