Identify Operation: Identify the operation to be performed on the given expressions. We are asked to find the sum of 2^204 and 2^204.Apply Exponent Property: Apply the property of exponents for terms with the same base and exponent when added together. When we add two identical terms, it is equivalent to multiplying the term by 2. So, 2^204 + 2^204 = 2 * 2^204.Simplify Using Laws: Simplify the expression using the laws of exponents. 2 * 2^204 can be written as 2^(1) * 2^204. According to the laws of exponents, when we multiply terms with the same base, we add the exponents. So, 2^(1) * 2^204 = 2^(1+204) = 2^205.Conclude with Answer: Conclude with the final answer. The sum of 2^204 and 2^204 is 2^205.

Algebra 2

Factor quadratics

Full solution

2^{204}+2^{204}

Identify Operation: Identify the operation to be performed on the given expressions. $\newline$ We are asked to find the sum of $2^{204}$ and $2^{204}$ .
Apply Exponent Property: Apply the property of exponents for terms with the same base and exponent when added together. $\newline$ When we add two identical terms, it is equivalent to multiplying the term by $2$ . $\newline$ So, $2^{204} + 2^{204} = 2 \times 2^{204}$ .
Simplify Using Laws: Simplify the expression using the laws of exponents. $\newline$ $2 \times 2^{204}$ can be written as $2^{1} \times 2^{204}$ . $\newline$ According to the laws of exponents, when we multiply terms with the same base, we add the exponents. $\newline$ So, $2^{1} \times 2^{204} = 2^{1+204} = 2^{205}$ .
Conclude with Answer: Conclude with the final answer. $\newline$ The sum of $2^{204}$ and $2^{204}$ is $2^{205}.$