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

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Answer 1 · 2016-08-22T18:00:01

#=4096#

#4*4^5#

#=4^6#

#=4096#

Answer 2 · 2016-08-22T18:08:51

#4^6#

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

#4^1 * 4^5#

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

#4^1 * 4^5 = 4^(1+5)#

#4^6#

And #4^6# is our final term with positive exponents.

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Let's look at this at a different angle.

First write out #4^5# and #4^1#.

#4^1 = 4#

#4^5 = 4*4*4*4*4#

Now multiply together.

#(4)*(4*4*4*4*4)#

#4*4*4*4*4*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*4^5 = 4^6#