Exponents with Multiplication and Division

When multiplying and dividing, only the bases have to be the same in order to combine like terms. When like bases are multiplied- three would be our base here.

We’re multiplying 3 squared times 3 cubed. The bases are alike. That means we add our integer exponents. The reason for this is 3 squared means 3 times 3 times 3 cubed (3 times 3 times 3).

When you multiply 3 squared times 3 cubed, you end up with 3 times itself 1, 2, 3, 4, 5 times. It would be 3 to the fifth, which you could then simplify further if necessary.

All we had to do was add our exponents, 2 plus 3 and 3 squared times 3 cubed. 3 to the fifth. When dividing with like bases, we subtract our exponent. Here’s the reason for that.

If you have 2 to the 6th divided by 2 to the fourth, then that’s 2 times itself 6 times. 1, 2, 3, 4, 5, 6 divided by 2 times itself four times, then 2 divided by 2 is 1.

2 divided by 2 is one. 2 divided by 2 is 1. 2 divided by 2 is 1. You’re left with just 2 times itself two times, or 2 squared. All we had to do was subtract our exponents.

2 to the sixth divided by 2 to the fourth is 2 squared, which, again, you could simplify further: 2 squared is 4. Our last one is when raising a power to a power.

When you raise a power to a power, you multiply the exponent. The reason for that is what we’re doing here is 5 squared times itself three times, which would be 5 squared times 5 squared times 5 squared.

5 squared is 5 times itself two times, times 5 squared (5 times itself two times) times 5 squared (5 times itself two times), and you end up with 5 times itself 1, 2, 3, 4, 5, 6 times.

All we had to do was multiply our exponents together. 5 squared cubed is 5 to the sixth. When multiplying with like bases, we add our exponents. When dividing with like bases, we subtract the exponent. When raising a power to a power, we multiply the exponent.