Given 10 ^ a = 2, 10 ^ B = 3. Find 100 ^ (2a-b)

Given 10 ^ a = 2, 10 ^ B = 3. Find 100 ^ (2a-b)

100^(2a-b)
=100^(2a)/100^b
=(10^a)^4/(10^b)^2
=2^4/3^2
=16/9

Factor multiplied by factor equals product

Yes!

In a multiplication formula, if one factor is multiplied by 10 and the other factor remains unchanged, the product () A. equals to the original product B equals to the original product
In a multiplication formula, if one factor is multiplied by 10 and the other factor remains unchanged, the product ()
A. Equal to the original product B equal to the original product multiplied by 10 C. equal to the original product divided by 10

Product invariant
For example: originally: 2 * 40 = 80
Now: (2 * 10) * (40 * 1 / 10) = 80