If 3x-y=12, what is the value of (8^(x))/(2^(y)) ? A) 2^(12) B) 4^(4) C) 8^(2) D) The value cannot be determined from the information given.

Given Equation: We are given the equation 3x - y = 12 and asked to find the value of (8^(x))/(2^(y)). First, let's simplify the expression using properties of exponents.Simplify Expression: Recall that 8 can be written as 2^3. So, 8^(x) can be rewritten as (2^3)^(x) which simplifies to 2^(3x) using the property of exponents that states (a^b)^c = a^(b*c).Apply Exponent Properties: Now, we have the expression 2^(3x) / 2^(y). Using the property of exponents that states a^(m) / a^(n) = a^(m-n), we can simplify this to 2^(3x - y).Substitute in Equation: Given the equation 3x - y = 12, we can substitute 12 for 3x - y in our expression. This gives us 2^(12).Final Value: Therefore, the value of (8^(x))/(2^(y)) given the equation 3x - y = 12 is 2^(12), which matches option A.

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Algebra 2

Evaluate expression when two complex numbers are given

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Q. If

3x-y=12

, what is the value of

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(8^{x})/(2^{y})

\newline

2^{12}

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4^{4}

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8^{2}

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D) The value cannot be determined from the information given.

Given Equation: We are given the equation $3x - y = 12$ and asked to find the value of $(8^{x})/(2^{y})$ . First, let's simplify the expression using properties of exponents.
Simplify Expression: Recall that $8$ can be written as $2^3$ . So, $8^{x}$ can be rewritten as $(2^3)^{x}$ which simplifies to $2^{3x}$ using the property of exponents that states $(a^b)^c = a^{b*c}$ .
Apply Exponent Properties: Now, we have the expression $2^{3x} / 2^{y}$ . Using the property of exponents that states $a^{m} / a^{n} = a^{m-n}$ , we can simplify this to $2^{3x - y}$ .
Substitute in Equation: Given the equation $3x - y = 12$ , we can substitute $12$ for $3x - y$ in our expression. This gives us $2^{12}$ .
Final Value: Therefore, the value of $(8^{x})/(2^{y})$ given the equation $3x - y = 12$ is $2^{12}$ , which matches option A.