How to simplify expression with exponents?

Question

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: $2^{48}$?

Answer 1

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

Answer 2

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

Answer 3

$2\cdot2^{45}+6\cdot2^45 = 2^{46}+3\cdot2^{46} = 2^{46}\cdot(1+3)$

Answer 4

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

Answer 5

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 $2^{48}$.

Answer 6

note that:

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

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