Module-1 Algebra - Mathematics Secondary Course - Exponents And Radicals Worksheet

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MODULE -
1
Exponents and Radicals
Algebra
Notes
2
EXPONENTS AND RADICALS
We have learnt about multiplication of two or more real numbers in the earlier lesson. You
can very easily write the following
4 × 4 × 4 = 64,11 × 11 × 11 × 11 = 14641 and
2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256
Think of the situation when 13 is to be multiplied 15 times. How difficult is it to write?
13 × 13 × 13 ×.................15 times?
This difficulty can be overcome by the introduction of exponential notation. In this lesson,
we shall explain the meaning of this notation, state and prove the laws of exponents and
learn to apply these. We shall also learn to express real numbers as product of powers of
prime numbers.
1/q
In the next part of this lesson, we shall give a meaning to the number a
as qth root of a.
We shall introduce you to radicals, index, radicand etc. Again, we shall learn the laws of
radicals and find the simplest form of a radical. We shall learn the meaning of the term
“rationalising factor’ and rationalise the denominators of given radicals.
OBJECTIVES
After studying this lesson, you will be able to
write a repeated multiplication in exponential notation and vice-versa;
identify the base and exponent of a number written in exponential notation;
express a natural number as a product of powers of prime numbers uniquely;
state the laws of exponents;
p
0,
–m
explain the meaning of a
a
and
a ;
q
simplify expressions involving exponents, using laws of exponents;
Mathematics Secondary Course
39

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