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One question left for me to answer and I am stuck on it.

How to simplify $2 \cdot 2^{45} + 6 \cdot 2^{45}$ to this: $2^{48}$?

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Note that $$ \begin {align*} 2 \cdot 2^{45} + 6 \cdot 2^{45} &= \left( 2 + 6 \right) \cdot 2^{45} \\&= 8 \cdot 2^{45} \\&= 2^3 \cdot 2^{45} \\&= 2^{3 + 45} \\&= 2^{48}. \end {align*} $$

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  • $\begingroup$ Now I see. I didn't knew I can do like that. Thank you. $\endgroup$
    – Mindee
    Dec 27 '14 at 22:36
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    $\begingroup$ @CommanderShepard You're welcome! If the answer is satisfactory, you can click the checkmark under the arrows to the left of the arrows when you can. :) $\endgroup$ Dec 27 '14 at 22:41
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$2\cdot2^{45}+6\cdot2^45 = 2^{46}+3\cdot2^{46} = 2^{46}\cdot(1+3)$

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Hint: $$2\times 2^{45}+6\times 2^{45}=(2+6)\times2^{45}$$

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Hint: $2a+6a=8a=2^3a$. Now put back $a=2^{45}$.

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You can write $2^{48}$ as $2^3 \cdot 2^{45}$ and $2^3 = 8$. $2 \cdot 2^{45} + 6 \cdot 2^{45} = 8 \cdot 2^{45}$, which equals to $2^{48}$.

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note that:

$$2 + 6 = 8 = 2^3$$

$$ 2^3* 2^{45} = 2^{48} $$

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