# How do you simplify 4*4^5 and write it using only positive exponents?

Aug 22, 2016

$= 4096$

#### Explanation:

$4 \cdot {4}^{5}$

$= {4}^{6}$

$= 4096$

Aug 22, 2016

${4}^{6}$

#### Explanation:

First, lets remember that $4$ is the same as ${4}^{1}$. We can rewrite as follows:

${4}^{1} \cdot {4}^{5}$

Now we can use a rule of exponents. When multiplying two bases, add the exponents.

${4}^{1} \cdot {4}^{5} = {4}^{1 + 5}$

${4}^{6}$

And ${4}^{6}$ is our final term with positive exponents.


Let's look at this at a different angle.

First write out ${4}^{5}$ and ${4}^{1}$.

${4}^{1} = 4$

${4}^{5} = 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4$

Now multiply together.

$\left(4\right) \cdot \left(4 \cdot 4 \cdot 4 \cdot 4 \cdot 4\right)$

$4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4$

If you count the $4$s, you will notice that there are a total of six of them. This can be rewritten as ${4}^{6}$. This matches our solution from above.

$4 \cdot {4}^{5} = {4}^{6}$