# Multiplication and division in different bases a relationship

### Math Forum - Ask Dr. Math

To divide exponents (or powers) with the same base, subtract the exponents. Division is the opposite of multiplication, so it makes sense that because you add . Multiplication and division are closely related, given that division is the inverse operation of multiplication. When we divide, we look to separate. High School Math Help» Algebra II» Mathematical Relationships and Basic Graphs . Recall that when we are dividing exponents with the same base, we keep the base the same .. Rewrite each side of the equation to only use a base 2.

**Other Bases Multiply**

You have a b over a b. Those guys cancel each other out. You have an x squared divided by an x, so x squared divided by x is x, and x divided by x is just a 1, so this becomes an x over 1, or just an x.

Finally, you have a y over a y squared. You divide the numerator by y, you get 1.

## Numbers in Different Bases

If you divide the denominator by y, you just get a y, and so what are we left with? We're left with in the numerator, these 1's we can ignore. That doesn't really change the number. We have a 7 times a times x. That's what we have in the numerator. In the denominator, we just have a 6y. And we have to add the constraint that a, b, x, and y cannot equal 0. For smaller bases, we use a subset of these digits. For example, in base 5, we only use digits ; in base 2 which is also called binarywe only use the digits 0 and 1.

## Smartick - Math, one click away

For larger bases, we need to have single digits for values past 9. Hexadecimal base 16 numbers provide an example of how this can be done. In this way, we have digits corresponding towhich is what we need.

In these instances, the context of their use usually makes the base clear. Changing from base 10 to a different base One straight-forward, but inefficient way to convert from base 10 to a different base is to: Determine the higest power of the base that goes into the number a non-zero number of times.

Thanks for asking it. I've never really thought about it that way!

### The Relation between Multiplication and Division - Elementary Math

Let's see what he might mean by it. Let's leave aside for the moment the continuous nature of both exponents and logarithms, e. If we know the exponent, we use a root to find the original base: The root is answering the question: If we multiply four copies of some quantity and get a product of 81, what would that quantity be? The logarithm is answering the question: If we multiply some number of copies of 3 and get a product of 81, what would that number be?

Now, suppose we decide we'd like to answer these numerically.