Examples of Solving Powers with Variables

The six rules of powers from the previous entries are useful in many cases. If you understand these crucial rules, you’ll be on the right track to mastering the mathematics that lies ahead.

Here are some examples combining all the rules. Make sure you understand them!

Example 1

Write (xy)3 x2y3 as simply as possible

(xy)3 x2y3 = x3y3x2y3 = x3+2y33 = x5y0 = x5 1 = x5

Example 2

Write (x y) 3 as simply as possible

(x y )3 = x3 y3 = 1 x3y3 = y3 x3

Note that you can actually just flip the fraction and change the sign of the exponent, like this:

(x y )3 = (y x)3 = y3 x3

Example 3

Write 33a3b(ab)3 as simply as possible

33a3b(ab)3 = 27a3ba3b3 = 27a3+3b1+3 = 27a0b4 = 27b4

Example 4

Write 2x2y2 2xy as simply as possible

2x2y2 2xy = 21x2y2 21x1y1 = 2121x2x1y2y1 1 = 211x21y21 = 20x1y1 = xy

Example 5

Write a2b422 (2ab)3 as simply as possible

a2b422 (2ab)3 = a2b422 23a3b3 = a2a3b4b32223 = a2+3b4+322+3 = a5b125 = 25a5 b

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