Rules of exponents for multiplication

Answer 1

The rule for multiplying with exponents

1) In order to multiply you must have the same base!

ex: 3^2 * 3^5

3 is the base.

When you multiply exponents, just add the exponents together and keep the same base.

3^2 * 3^5 = 3^7

Visually, this is what it looks like.

3^2 = 3 * 3

3^5 = 3*3*3*3*3

Since we're multiplying them together...

3*3 *( 3*3*3*3*3)

All we do is count up how many times we're multiplying 3 by itself.

I count 7 times. That means 3 is being raised to the 7th power, or 3^7.

When you have an exponent raised to another exponent:

example (5²)³ [five squared, then cubed], if you work it out long way:

(5 * 5)³ = (5 * 5) * (5 * 5) * (5 * 5) = 56, so you multiply the exponents (2 * 6). This is just like multiplying being the same as repetitive addition.