# How do you determine which is greater #4^2*4^3 (<=>) 4^5#?

##### 3 Answers

#### Explanation:

One of the properties of exponents says that

Hence

Hence we can say that

They are equal.

#### Explanation:

The rule says that the multiplication of powers of a same base is the base elevated to the sum of the powers. In formulas:

Apply the definition of power:

Multiply the two numbers:

So, no one of the two numbers is greater than the other, they are exactly the same.

Based on an assumption: They are the same!

#### Explanation:

Assumption: by the dot you mean multiply.

Consider

Now consider

Now consider both parts (1) and (2) together:

(2) may be rewritten as

but we know that (2) is also

From this we can deduce that

Ok! now look at the question given:

We have

By using the same approach as before this would give us:

In conclusion: both sides of