Workout: $$ 2^{2} imes 2^{8 x}=2^{-3} $$

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Workout: $$ 2^{2} 	imes 2^{8 x}=2^{-3} $$

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The solution is $$ x = -\frac{5}{8} $$. To solve the equation $$ 2^{2} \times 2^{8x} = 2^{-3} $$, we can use the properties of exponents. Specifically, we can combine the exponents on the left side of the equation. Using the property $$ a^m \times a^n = a^{m+n} $$, we can rewrite the left side: $$ 2^{2 + 8x} = 2^{-3} $$ Now that we have the same base on both sides of the equation, we can set the exponents equal to each other: $$ 2 + 8x = -3 $$ Next, we will solve for $$ x $$. First, subtract 2 from both sides: $$ 8x = -3 - 2 $$ $$ 8x = -5 $$ Now, divide both sides by 8: $$ x = \frac{-5}{8} $$ Thus, the solution is: $$ \boxed{-\frac{5}{8}} $$

Workout: \( 2^{2} \times 2^{8 x}=2^{-3} \)

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Workout: \( 2^{2} \times 2^{8 x}=2^{-3} \)

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