how do you do division exponents with positive exponents

#How do you do division exponents with positive exponents full#

Thanks to the calculation above, we can familiarize ourselves with the third essential rule of exponents: the Power Rule. Writing it another way, we can see that (X3)4 equals to X(3 x 4) Thus, we can determine that (X3)4 equals X12. This way, we can assign the outer exponent of '4' into each X.įinally, using the Product Rule, let's combine the exponents into one. If it's too confusing, let's break it down into a more tangible form.įirst, we expand the exponent inside the parentheses. Our next topic looks at a base with a visible exponent raised to a certain power. In our case, the bases are the same variable of 'X'. Identical to the Product Rule, the Quotient Rule can only work if all of the bases have the same value. Once again, our work brings us to the second rule of exponents: the Quotient Rule. Or, we can also write it as X6/X3 equals X(6 - 3).

#How do you do division exponents with positive exponents full#

We can gather all of the steps together to see the full picture. Consider this expression.īy this point, you might have understood that we can expand the bases to reveal their copies based on the value of each exponent.įrom here, we can erase three Xs from both the numerator and denominator of the fraction. If the Product Rule lets us add two exponents together, the Quotient Rule would instead grant us the ability subtract two exponents. Putting all of them together, we can determine that the value of (x5 y6)(x2 y) equals to (x7)(y7). Why? Because anything to the power of 1 has 'one copy' of itself. All numbers have the power of 1 if there is no exponent explicitly written above it. Once they have grouped nicely, we can apply the product rule by adding up the exponents with the same base.ĭid you see what happened? For the base of 'y', we add the exponent of 6 and 1, even though the second 'y' doesn't seem to have an exponent.įor any number or variable that doesn't have an exponent written above it, it has an exponent of 1. To solve this problem, first, let's group the same variables. To improve our understanding, let's pay attention to some more advanced examples of multiplying variables with different exponents. In the example before, the exponents of 4 and 7 have the same base: 'X'. Keep in mind that the rule above only applies if the bases of the two exponents are the same. The calculation above introduces us to a basic exponent rule called ' Product Rule': To make this more intuitive, we can also write it as (X4)(X7) equals X(4 + 7). You can also simplify things by replacing the result with 'X11'. There are 11 copies of the same variable. How many X on the right side of the equal symbol? Bingo! It's 11. To simplify things further, let's remove the unnecessary parentheses. The number of variables written equals the value of each exponent.

You can see that we expand the variables with exponents into different amounts of variable iterations. Multiplying X with different exponents means that you multiply the same variables-in this case, 'X'-but a different amount of times. Multiplying X with Different Exponents Product Rule Once you understand these basic concepts, we can move on to the main topic. In Algebra, putting two or more variables next to each other means multiplying them. The number 4 is raised to the third power or cubed. Do you know the value of 43?Ĥ3 means 4 times 4 times 4. Let's use a simple example using an integer instead of variable for the base. The number or variable we multiply is called the base. The exponent tells us how many times it uses a number or variable in multiplication. On the other hand, the number 3 above ' x' in ' x3' is what people call an exponent. The most common symbols used in most equations are x, y, and z. In another equation, x may be equal to 7 or a more complicated number like 75/2. The value of x may vary (hence the name). X is a variable, or something that has an unknown value. Do you still remember the concept of variables and exponents? Before we jump into the topic in question, let's review.