Is there a way to prove this in upwards of 5 steps? Apparently there is??
Prove.
2^n + 2^n = 2^(n+1)
I posted this before however apparently I need something more indepth in terms of the # of steps.
A quantity of oxygen gas had 16.32 g of the radioactive isotope oxygen-19 in it. When measured exactly 10 minutes later, the amount of oxygen-19 was 0.964 g. What is the half-life, in seconds, of oxygen-19?
woops
let me repost this elsewhere
LS = 2^n + 2^n
= 2(2^n)
= 2(n+1)
= RS
To prove the equation 2^n + 2^n = 2^(n+1), we can follow these steps:
Step 1: Start with the left side of the equation: 2^n + 2^n.
Step 2: Write 2^n as 2 × 2^(n-1) (based on the exponent rule that a^n + a^n = 2 × a^n).
Step 3: Apply the distributive property to the equation, which gives us 2 × 2^(n-1) + 2 × 2^(n-1).
Step 4: Combine like terms. The terms 2 × 2^(n-1) and 2 × 2^(n-1) are identical, so we add them together, resulting in 4 × 2^(n-1).
Step 5: Rewrite 4 × 2^(n-1) as 2^2 × 2^(n-1), or 2^(n-1+2).
Step 6: Apply the exponent rule that states a^m × a^n = a^(m+n) to simplify the equation, obtaining 2^(n-1+2) = 2^(n+1).
Hence, we have successfully proven that 2^n + 2^n = 2^(n+1) using these six steps.