# How do you simplify 2^7+2^4?

Mar 6, 2018

The answer is $144$.

#### Explanation:

In standard form, ${2}^{7}$ would be $2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$ which equals $128$.

And ${2}^{4}$ would be $2 \times 2 \times 2 \times 2$ and it equals $16$.

$128 + 16 = 144$

${2}^{7} + {2}^{4} = 144$

#### Explanation:

${2}^{7} + {2}^{4} = {2}^{4 + 3} + {2}^{4}$
$= {2}^{4} \times {2}^{3} + {2}^{4}$
$= {2}^{4} \times \left({2}^{3} + 1\right)$
${2}^{3} = 8 , {2}^{4} = 16$
${2}^{3} \times \left({2}^{4} + 1\right) = 16 \times \left(8 + 1\right)$
$= 16 \times 9$
$= 144$
Hence,
${2}^{7} + {2}^{4} = 144$

Mar 6, 2018

$144$

#### Explanation:

Compare ${2}^{7} + {2}^{4}$ with ${x}^{7} + {x}^{4}$

We can factorise ${x}^{7} + {x}^{4}$

$= {x}^{4} \left({x}^{3} + 1\right) \text{ } \leftarrow$ cannot be simplified further

Do the same with ${2}^{7} + {2}^{4}$

$= {2}^{4} \left({2}^{3} + 1\right) \text{ } \leftarrow$ they are values and can be calculated:

$= 16 \left(8 + 1\right)$

$= 16 \times 9$

$= 144$