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Introduction and Summary

Exponents play a large role in mathematical calculations. This chapter
provides an introduction to the meaning of exponents and the calculations
associated with them. Since exponents are used abundantly in all of
mathematics, the basics taught in this chapter will become important building
blocks for future knowledge.

The first section will
explain the fundamentals of exponents, and explore squares, cubes, and
higher order exponents. This section will explain how to square and cube
numbers, as well as how to recognize a perfect square.

The second section will focus
on exponents applied to specific types of numbers--namely, negative
numbers, decimals, and
fractions. Here, we will learn how to raise
these base numbers to any power.

The third section will
explore calculations in which the *exponent* is negative. It will explain
the meaning of a negative exponent and how to evaluate expressions that contain
negative exponents. It will also show the importance of negative exponents to
the base ten system while discussing how
write out any terminating decimal as a sum
of single-digit numbers times powers of ten.

The fourth section will deal
with roots--square roots, cube roots, and higher order roots--and
fractional exponents. This section will explain what a root is and how
to find a root if the answer is
rational. It will
also explain why we cannot take the square root (or any even root) of a
negative number. This section will also explain how to raise a number to a
fractional power.

The fifth section will deal
with roots that are not easy to find. It first shows how to simplify a
square root to make calculations easier, and it then shows how to find an
approximate decimal value for a square root.

The final section will
revisit the order of operations
learned
in the SparkNote on Operations, and
revise this order to include calculations with exponents.

Overall, this chapter offers an introduction to exponents for those readers who
have never been exposed to them, and an opportunity to sharpen knowledge to
those who have. Exponents will play an important role in pre-algebra during
area calculations. They will also
be very important in future mathematical endeavors, including
algebra, geometry, calculus, and higher mathematics.