Algebra Know-It-ALL

Now it’s time to review and expand your knowledge of powers and roots. When you take a

number to an integer power, it’s like repeated multiplication. When you take a number to

an integer root, it’s like repeated division. But powers and roots go deeper than that! With

a few exceptions, you can raise anything to a rational-number power and get a meaningful

result.

Integer Powers

The simplest powers, also called exponential operations, involve multiplying a number or quan-

tity by itself a certain number of times. The power is written as a superscript after the quantity

to be “operated on.” This operation is sometimes called raising to a power.

Positive integer powers

If a is any number and p is a positive integer, the expression ap means a to the pth power,

which is a multiplied by itself p times. More generally, a doesn’t have to be a number. It can

be a variable or a complicated expression containing numbers and variables. Here are some

examples of quantities raised to positive integer powers:

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x^4

(k+ 4)^7

(abc)^4

(m/n)^12 where n≠ 0

(x^2 − 2 x+ 1)^5

Note that in the last expression, the quantity raised to the 5th power actually contains a vari-

able raised to a different power.

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CHAPTER

8 Powers and Roots

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