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

Given Equation: We are given the equation 3x - y = 12. We need to find the value of (8^(x))/(2^(y)). First, let's express 8 in terms of 2, since 8 is 2 to the power of 3. 8 = 2^3Expressing 8 in Terms of 2: Now, let's substitute 8 with 2^3 in the expression (8^(x))/(2^(y)). (8^(x))/(2^(y)) = ((2^3)^(x))/(2^(y))Substitute 8 with 2^3: Using the power of a power rule, which states that (a^(m))^n = a^(mn), we can simplify the numerator. ((2^3)^(x)) = 2^(3x)Simplify the Numerator: Now, the expression looks like this: (2^(3x))/(2^(y))Final Expression: Using the quotient of powers rule, which states that a^(m)/a^(n) = a^(m-n), we can simplify the expression further. (2^(3x))/(2^(y)) = 2^(3x - y)Substitute Given Value: We know from the given equation that 3x - y = 12. Let's substitute this value into our expression. 2^(3x - y) = 2^(12)Final Value: Therefore, the value of (8^(x))/(2^(y)) is 2^(12), which corresponds to option A.

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If $3x-y=12$ , what is the value of $\newline$ $(8^{x})/(2^{y})$ ? $\newline$ A) $2^{12}$ $\newline$ B) $4^{4}$ $\newline$ C) $8^{2}$ $\newline$ D) The value cannot be determined from the

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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

\newline

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

\newline

2^{12}

\newline

4^{4}

\newline

8^{2}

\newline

D) The value cannot be determined from the

Given Equation: We are given the equation $3x - y = 12$ . We need to find the value of $(8^{x})/(2^{y})$ . $\newline$ First, let's express $8$ in terms of $2$ , since $8$ is $2$ to the power of $3$ . $\newline$ $8 = 2^3$
Expressing $8$ in Terms of $2$ : Now, let's substitute $8$ with $2^3$ in the expression $(8^{x})/(2^{y})$ . $\newline$ $($8$^{x})/($2$^{y}) = (($2$^$3$)^{x})/($2$^{y})
Substitute $8$ with $2^3$: Using the power of a power rule, which states that $(a^{(m)})^n = a^{(mn)}$, we can simplify the numerator.$\newline$$((2^3)^{x}) = 2^{(3x)}$
Simplify the Numerator: Now, the expression looks like this: $\newline$$(2^{3x})/(2^{y})$
Final Expression: Using the quotient of powers rule, which states that $a^{m}/a^{n} = a^{m-n}$, we can simplify the expression further.$\newline$$(2^{3x})/(2^{y}) = 2^{3x - y}$
Substitute Given Value: We know from the given equation that $3x - y = 12$. Let's substitute this value into our expression.$\newline$$2^{3x - y} = 2^{12}$
Final Value: Therefore, the value of $\frac{8^{x}}{2^{y}}$ is $2^{12}$, which corresponds to option A.