2^(203)+2^(204) Which of the following values is equal to the value? Choose 1 answer: (A) 2^(407) (B) 3(2^(203)) (C) 3(2^(204)) (D) 2^(202)+2^(205)

Recognize Exponential Rule: Recognize that 2^(204) is the same as 2^(203) * 2^(1).Calculate 2^204: Calculate 2^(204) by multiplying 2^(203) by 2. 2^(204) = 2^(203) * 2Add Exponentials: Add 2^(203) and 2^(204) together. 2^(203) + 2^(204) = 2^(203) + 2 * 2^(203)Factor Out Common Term: Factor out the common term 2^(203). 2^(203) + 2 * 2^(203) = 2^(203) * (1 + 2)Simplify Expression: Simplify the expression inside the parentheses. 1 + 2 = 3Multiply by 3: Multiply 2^(203) by 3. 2^(203) * 3 = 3 * 2^(203)Compare with Options: Compare the result with the given options. The result 3 * 2^(203) matches option (B).

Home

Math Problems

Algebra 1

Negative exponents

Full solution

2^{203}+2^{204}

\newline

Which of the following values is equal to the value?

\newline

Choose

1

answer:

\newline

(A)

2^{407}

\newline

(B)

3\left(2^{203}\right)

\newline

(C)

3\left(2^{204}\right)

\newline

(D)

2^{202}+2^{205}

Recognize Exponential Rule: Recognize that $2^{204}$ is the same as $2^{203} \times 2^{1}$ .
Calculate $2^{204}$ : Calculate $2^{204}$ by multiplying $2^{203}$ by $2$ . $\newline$ $2^{204} = 2^{203} \times 2$
Add Exponentials: Add $2^{203}$ and $2^{204}$ together. $\newline$ $2^{203} + 2^{204} = 2^{203} + 2 \times 2^{203}$
Factor Out Common Term: Factor out the common term $2^{203}$ . $2^{203} + 2 \times 2^{203} = 2^{203} \times (1 + 2)$
Simplify Expression: Simplify the expression inside the parentheses. $\newline$ $1 + 2 = 3$
Multiply by $3$ : Multiply $2^{203}$ by $3$ . $\newline$ $2^{203} \times 3 = 3 \times 2^{203}$
Compare with Options: Compare the result with the given options. $\newline$ The result $3 \times 2^{203}$ matches option (B).