Evaluate the expression (4^(x))/(2^(x)) for x=3.

Recognize the base: Recognize that 4 can be expressed as 2 squared, so 4^x = (2^2)^x. Apply power of a power rule: Apply the power of a power rule, which states that (a^b)^c = a^(b*c). Therefore, (2^2)^x = 2^(2*x). Substitute x with 3: Substitute x with 3 into the expression 2^(2*x) to get 2^(2*3) which simplifies to 2^6. Apply quotient rule for exponents: Now we have the expression (2^6)/(2^3). Apply the quotient rule for exponents, which states that a^(m)/a^(n) = a^(m-n) when a ≠ 0. Subtract the exponents: Subtract the exponents: 6 - 3 = 3. So, (2^6)/(2^3) = 2^(6-3) = 2^3. Calculate the final answer: Calculate 2^3 to get the final answer. 2^3 = 2 * 2 * 2 = 8.

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Evaluate the expression
(4^(x))/(2^(x)) for
x=3.

Evaluate the expression $\frac{4^{x}}{2^{x}}$ for $x=3$ .

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Q. Evaluate the expression

\frac{4^{x}}{2^{x}}

for

x=3

Recognize the base: Recognize that $4$ can be expressed as $2$ squared, so $4^x = (2^2)^x$ .
Apply power of a power rule: Apply the power of a power rule, which states that $(a^b)^c = a^{(b*c)}$ . Therefore, $(2^2)^x = 2^{(2*x)}$ .
Substitute $x$ with $3$ : Substitute $x$ with $3$ into the expression $2^{2\cdot x}$ to get $2^{2\cdot 3}$ which simplifies to $2^6$ .
Apply quotient rule for exponents: Now we have the expression $(2^6)/(2^3)$ . Apply the quotient rule for exponents, which states that $a^{m}/a^{n} = a^{(m-n)}$ when $a \neq 0$ .
Subtract the exponents: Subtract the exponents: $6 - 3 = 3$ . So, $(2^6)/(2^3) = 2^{(6-3)} = 2^3$ .
Calculate the final answer: Calculate $2^3$ to get the final answer. $2^3 = 2 \times 2 \times 2 = 8$ .