# Expressions - How to Multiply and DivideAlgebraic Expressions

## Expressions - Multiplying and Dividing - How it Works - Video

### Example 1

Example 1:

Here we are simplifying expressions when only multiplication is involved. The expression is (4ab)(3a). The first step is drop to the parenthesis since none of the parenthesis are being raised to a power. The next step is to rearrange the like terms in order to give a better perspective on what is happening. Now we have 4 *3*a*a*b. We can multiply the 4 and 3 to make 12. Now we have 12*a*a*b. There are hidden exponents for a and it is 1 for each letter. If we add the hidden exponents or 1 for each a, we get 2 because 1 + 1 = 2. We can do this because of the Multiplication Rule of Exponents. So our answer is 12*a^2*b.

### Example 2

Example 2:

Here we are simplifying expressions when only multiplication is involved. The expression is (3ab)(2a^2)(5b)^2. The fist step is rewrite (5b)^2 so our exponent is 1. The exponent tells us that we can rewrite it twice. So now we have (3ab)(2a^2)(5b)(5b). Now we can drop the parenthesis since none of the parenthesis are being raised to a power. The next step is rearrange so the like terms are next to each other. So now we have 3*2*5*5*a*a^2*b*b*b. We multiply the numbers, 3*2*5*5, to get 150. Now we add the exponents of like terms, because of the Multiplication Rule of Exponents. For a, we have 1 + 2 = 3 and for b, we have 1 + 1 + 1 = 3. So our answer is 150*a^3*b^3.

### Example 3

Example 3:

Here we are simplifying expressions when only multiplication is involved. The expression is (8xy^2)(2y^2)(3x^2y)^4. Instead of writing the term (3x^2y) four times, we are going to use the Product Rule of Exponents. Now we can write the expression as 3^4*x^8*y^4. We multiply the exponents to get the answer so the hidden 1 for the 3 times the 4 (1*4) to get 3^4; 2 for the x^2 times the 4 (2*4) to get x^8; the hidden 1 for the y times the 4 (1*4) to get y^4. Now we can drop the parenthesis since none of the parenthesis are being raised to a power. The next step is rearrange so the like terms are next to each other. So now we have 8*2*81*x*x^8*y^2*y^2*y^4. Now multiply the numbers, 8*2*81, to get 1296. Now we add the exponents of like terms, because of the Multiplication Rule of Exponents. For x, we have the hidden 1 + 8 = 9 and for y, we have 2 + 2 + 4 = 8. So our answer is 1296*x^9*y^8.

### Example 4

Example 4:

Here we are simplifying expressions when only multiplication is involved. The expression is (5x^4y^3)/(4x^2y). In the picture we have written out all the variables based on their exponents to cancel the terms. Since there are 4 x's on top and 2 x's on bottom, we can cancel 2 of them. Instead of writing the variables each time, we can use the Division Rule of Exponents, where we can subtract the exponents if one like term is one top and one is bottom. So we have x^4 and x^2, we can subtract 4 - 2 to get 2 so we get x^2 on the top. We can do the same to the variable, y, because we have y^3 on top and y^1 on bottom. We can subtract 3 - 1 to get 2 and we get y^2 on the top. So our final answer is (5*x^2*y^2)/4.

### Example 5

Example 5:

Here we are simplifying expressions when only multiplication is involved. The expression is (4x^1y^3)/(8x^5y^2). In the picture we have written out all the variables based on their exponents to cancel the terms. Since there are 1 x on top and 5 x's on bottom, we can cancel 1 of them. Instead of writing the variables each time, we can use the Division Rule of Exponents, where we can subtract the exponents if one like term is one top and one is bottom. So we have x^1 and x^5, we can subtract 5 - 1 to get 4 so we get x^4 on the bottom. We can do the same to the variable, y, because we have y^3 on top and y^2 on bottom. We can subtract 3 - 2 to get 1 and we get y^1. Now we have to divide the 4 and 8 by 4 since both of those numbers are multiples of 4. 4 divided by 4 is 1 and 8 divided by 4 is 2. So our final answer is y/(2x^4).
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