How many times as large as 4^4 is 4^7

Step-by-step explanation:

Note that 4^7 = 4^4*4^3.  

Compare 4^4 and 4^4 * 4^3.  The last factor is 64.  So 4^7 is 64 times larger than 4^4.

256

Step-by-step explanation:

So, there are a few different ways to solve this.

Firstly, you need to find the values of these numbers.

4^4 = 4x4x4x4 = 4x4 = 16x4 = 64 x 4 = 256.

4^7 = 4x4x4x4x4x4x4 = 4x4 = 16x4 = 64x4 = 256x4= 1,024x4=4,096x4 = 16,384.

Now, divide 16,384 by 256:

16,384/256

=

64

This is your answer.

Now, WHY do we have to use such a slow painful way of doing this? There MUST be a better way!

Well, there is.

Remember two things.

Dividing exponents is actually subtracting 1 exponent from the other.

Multiplying exponenets is actually adding 1 exponent to another.

Adding and subtracting is still adding and subtracting like normal.

This problem calls for division.

So, all we need to do is subtract 4^7 by 4^4:

4^7-4

=

4^3

What does 4^3 equal?

64!

This is far easier and quiocker, and won't burn a hole through your brain!

Hope this helps! :)