Integers are positive or negative whole numbers. To multiply an integer, simply multiply the two numbers. If you have an even number of negative numbers which you are multiplying, your answer will be positive. If you are multiplying an odd number of negative integers, your answer will be negative. Exponents tell you how many times you are multiplying a single term. So, 2^3 would be 2 x 2 x 2. To multiply exponents, add the exponents. Thus, 2^3 x 2^5 would be 2^8.
Write down your terms to be multiplied. For example, 3^3 x 3^2 x 5^4 x 5^8.
Add the exponents for like terms. You can not multiply the exponents of unlike terms. For the example, you would get 3^5 x 5^12. If you write it out, 3 x 3 x 3 x 3 x 3 you will see that three 3s multiplied by two 3s will give you five 3s. But some exponents are larger and it would be impractical to write them all out.
Add exponents that are variables. Variable exponents work the same way as constant exponents. 3^n x 3^n would be 3^2n.
Put numbers with negative exponents in fraction form. For example, 3^-2 would be written as 1/3^2. Conversely, 1/3^-2 would become 3^2. You must still add the exponents to multiply. 3^-2 x 3^2 would be 3^0 and any number with an exponent (0) is equal to one.
Check if your exponent is odd or even. A negative number with an even exponent will be positive when calculated, and a negative number with an odd exponent will be negative when multiplied out. For example: -2^3 is -8 and -2^2 is +4.