Question

How do you do this I don’t understand it

Answer 1

When multiplying powers with the same base but different exponents, just add the exponents together. Note: this can only work if the base is the same. Note2: you can do the same with dividing powers by subtracting the exponents instead of adding.

Ex: 1. 2^7*2^2 (2 is the base, 7&2 are the exponents.
2^7*2^2 = 2^9 (add 7&2)
2^9 = 512

Answer 2

Step-by-step explanation:

Let's look at #1 as an example.

The question asks us to find the product of $2^7*2^2$

One way to look at this product is however many 2's being multiplied together. That would look as so

$(2*2*2*2*2*2*2)*(2*2)$

This would simplify to

$2*2*2*2*2*2*2*2*2$

As there are 9 2's being multiplied together, we can write this as

$2^9$

This, however is the long and hard way to do each of these problems.

We began with $2^7*2^2$ and ended with $2^9$

As we can see, our answer was just the sum of the exponents.

Now that we know that when you multiply two exponents with the same bases, all you have to do is add the powers, you should be able to do the rest of the problems.