GMATPrep Problem

Hello,

Just divide the LHS by 2 and the equation becomes :

5^21 * 2^21 = 10 ^ n

=> 10^21 = 10^n

n = 21.

thanks!

Can someone explain this to me? I thought when you multiply powers you add them together?

Can someone explain this to me? I thought when you multiply powers you add them together?

Jeffers wrote:Can someone explain this to me? I thought when you multiply powers you add them together?

When we multiply two powers with the same base, we add the exponents.

However, when we multiply two bases with the same power, we multiply the bases and the power stays the same.

So:

2^21 * 5^21 = (2*5)^21 = 10^21

To help understand this, we can visualize 2^21 as a string of 21 2s, multiplied together. Similarly, we can visualize 5^21 as a string of 21 5s, multiplied together.

So, 2^21 * 5^21 is really just 21 2s and then 21 5s, all multiplied together.

Instead of writing all the 2s in a row and all the 5s in a row, we could have alternated them (since for multiplication, the order of terms is irrelevant).

So, we can visualize a string of 2*5*2*5*2*5... that contains 21 2s and 21 5s in total.

Now, let's put brackets around each pair of terms to get:

(2*5)*(2*5)*(2*5)... and we'll have 21 bracketed pairs.

Since 2*5 = 10 we can rewrite this as:

(10)*(10)*(10).... with 21 10s in a row, which of course we can rewrite as:

10^21.

Hope that helps!

It does thank you!