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Multiplication and Fractions with Powers

The terms a3 and 7a2 cannot be simplified. These powers are of different degrees, so they don’t have the same variable combination! Remember—you can’t simplify two powers even if they have the same variable, if they are of different degrees.

With a2 and 6a2, on the other hand, those can be simplified to 7a2. This is because the variables are the same—a—and they’re the same degree, the second power.

Below, you can see how to cancel equal variables out against each other in a fraction.

Example 1

Simplify 4x3 2x x

There are many ways to simplify this expression, and now you’ll look at several rules about calculating with powers.

You begin by simplifying the numerator:

4x3 2x = 4 2 x3 x = 8x4

The expression then becomes

8x4 x = 8 x x x x x = 8x3

Example 2

Simplify 4x a 2a x

You use the flip formula to simplify the expression, and get

4x a 2a x = 4x a ÷ 2a x = 4x a x 2a = 4x2 2a2 = 2x2 a2

4x a 2a x = 4x a ÷ 2a x = 4x a x 2a = 4x2 2a2 = 2x2 a2

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