CL-8 Exponents and Powers

2. Introduction to Exponents and Powers
The exponents tell us that how many times the number should
be multiplied. It is called the Exponential form. This is written
like this:
Here 10 is the base and 9 is the exponent and this complete
number is the power. We pronounce it as 10 raised to the
power 9. The exponent could be positive or negative.
This tells us that the number 10 will be multiplied 9 times, like,
10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10

3. Powers with Negative Exponents
A negative exponent is defined as the multiplicative inverse of the
base, raised to the power which is opposite to the given power. In
simple words, we write the reciprocal of the number and then solve it
like positive exponents. For example, (2/3)-2 can be written as (3/2)2.

4. LAWS OF EXPONENTS

7. SUMS OF EX:12.1
Question 1.
Evaluate:
(i) 3-2
(ii) (-4)-2
(iii) (12)-5
Solution:

8. Question 2.
Simplify and express the result in power notation with a positive exponent.
Solution:

9. Question 3.
Find the value of
Solution:

10. Question 4.
Evaluate Solution:

11. Question 5.
Find the value of m for which 5m ÷ 5-3 = 55.
Solution:
5m ÷ 5-3 = 55
⇒ 5m-(-3) = 55 [∵ am ÷ an = am-n]
⇒ 5m+3 = 55
Comparing the powers of equal bases, we have
m + 3 = 5
m = 5 – 3 = 2, i.e., m = 2

12. Question 6.
Evaluate:
Solution:

13. Question 7.
Simplify:
Solution:

14. Use of Exponents to Express Small Numbers in Standard Form
 Scientific notation/Standard notation is just a short hand way of
expressing gigantic numbers like 1,300,000 or incredibly small numbers
like 0.0000000000045.
 Also known as exponential form, scientific notation has been one of the
oldest mathematical approaches.
 If numbers are too big or too small to be simply calculated, people reffer
to scientific notation to handle these circumstances. This method is
used by engineers, mathematicians, scientists.
 An example of scientific notation is 1.3 ×106 which is just a different way
of expressing the standard notation of the number 1,300,000.
 1.98 ✕ 10¹³; 0.76 ✕ 10¹³ are examples of numbers in standard form.

16. Complete Pg: 198 (12.4) till Q.12 and Pg: 200 Ex: 12.2 Q.1 to 4