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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

User Colm Troy
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2 Answers

4 votes

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.

Explanation:

User Justin Newbury
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4.0k points
2 votes

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

What is the value of y in the product of powers below? 8 cubed times 8 Superscript-example-1
User Aurore
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