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

Combine Powers of 8: Combine the powers of 8 using the property of exponents that states when you multiply powers with the same base, you add the exponents. 8^(3) * 8^(-5) * 8^(y) = 8^(3 - 5 + y)Simplify Exponents: Simplify the exponents by adding 3 and -5. 8^(3 - 5 + y) = 8^(-2 + y) 8^(-2 + y) = 8^(-2)Apply Exponent Rule: Since the bases are the same and the equation is an equality, the exponents must be equal. -2 + y = -2Solve for y: Solve for y by adding 2 to both sides of the equation. -2 + y + 2 = -2 + 2 y = 0

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

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

Combine Powers of $8$ : Combine the powers of $8$ using the property of exponents that states when you multiply powers with the same base, you add the exponents. $\newline$ $8^{3} \times 8^{-5} \times 8^{y} = 8^{3 - 5 + y}$
Simplify Exponents: Simplify the exponents by adding $3$ and $-5$ . $\newline$ $8^{(3 - 5 + y)} = 8^{(-2 + y)}$ $\newline$ $8^{(-2 + y)} = 8^{(-2)}$
Apply Exponent Rule: Since the bases are the same and the equation is an equality, the exponents must be equal. $\newline$ $-2 + y = -2$
Solve for y: Solve for y by adding $2$ to both sides of the equation. $\newline$ $-2 + y + 2 = -2 + 2$ $\newline$ $y = 0$