Can i multiply exponents

When you multiply two variables or numbers or with different bases but with the same exponent , you can simply multiply the bases and use the same exponent. For example:. If you have exponential numbers that are multiplied by other numbers, you can easily do the arithmetic. For example, simplify:. When you multiply expressions with different bases and different exponents , there is no rule to simplify the process. When you multiply two numbers or variables with the same base, you simply add the exponents.

When you multiply expressions with the same exponent but different bases, you multiply the bases and use the same exponent. When you multiply expressions with different bases and different exponents, there is no rule to simplify the process. Exponents: Basic Rules - PurpleMath. Not'n Eng. Not'n Fractional. Exponents are shorthand for repeated multiplication of the same thing by itself.

The "exponent", being 3 in this example, stands for however many times the value is being multiplied. The thing that's being multiplied, being 5 in this example, is called the "base". This process of using exponents is called "raising to a power", where the exponent is the "power". The expression " 5 3 " is pronounced as "five, raised to the third power" or "five to the third". Exponents: Basic Rules: Product Rule. There are two specially-named powers: "to the second power" is generally pronounced as "squared", and "to the third power" is generally pronounced as "cubed".

So " 5 3 " is commonly pronounced as "five cubed". When we deal with numbers, we usually just simplify; we'd rather deal with " 27 " than with " 3 3 ". To simplify this, I can think in terms of what those exponents mean.

Using this fact, I can "expand" the two factors, and then work backwards to the simplified form. First, I expand:. This is seven copies of the variable.

Then the simplified form of x 3 x 4 is:. This demonstrates the first basic exponent rule:. Nothing combines. Now that I know the rule namely, that I can add the powers on the same base , I can start by moving the bases around to get all the same bases next to each other:.

Now I want to add the powers on the a 's and the b 's. However, the second a doesn't seem to have a power. What do I add for this term? Anything that has no power on it, in a technical sense, being "raised to the power 1 ". If it's only multiplied one time, then it's logical that it equals itself. Secondly, one raised to any power is one. This, too, is logical, because one times one times one, as many times as you multiply it, is always equal to one.

Product Rule. The exponent "product rule" tells us that, when multiplying two powers that have the same base, you can add the exponents. In this example, you can see how it works. Adding the exponents is just a short cut!

Power Rule. The "power rule" tells us that to raise a power to a power, just multiply the exponents. Here you see that 5 2 raised to the 3rd power is equal to 5 6. Quotient Rule.