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Polynomial Exponents

Multiplication and Division

Examine the problem below.

(x3y4)5

Recall that multiplication is implied when there is no sign between a variable or set of parentheses and a number, another variable, or another set of parentheses. Therefore in this problem, the x3 and y4 are being multiplied.

In the next problem the x2 and x are being multiplied. The difference is that a * is present which explicitly indicates multiplication. We will solve this problem, then return to the first problem on the page.

(x2 * x)3

Because there is no addition or subtraction inside the parentheses, the exponent can be just "distributed" in and simplified:

(x2*3 * x3)
x6 * x3
x9

Notice that this gives the same result as if we had simplified the inside of the parentheses first, as we have done below.

(x2 * x)3
(x3)3
x3*3
x9

So why are there two different methods of solving this problem? The first method, where the exponent was distributed in can be applied to the first problem on this page, whereas the second method cannot.

We will now apply the "distribute in" method to the first problem presented on this page.

(x3y4)5
(x3*5y4*5)
x15y20

This method will also work when the terms are being divided, like the problem below:

(x2 / x)3

Again, the exponent is just "distributed" in:

(x2*3 / x3)
(x6 / x3)
x3

The next page explains what to do when you encounter fractions.


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