NCERT Solutions Maths Ch-12 Exponents and Powers for Class 8th
Here’s a summary of key concepts and some example problems from Chapter 12: Exponents and Powers, as per the NCERT syllabus for Class 8.
Definition of Exponents: An exponent indicates how many times a number (the base) is multiplied by itself.
Laws of Exponents:
- Product of Powers: When multiplying two expressions with the same base, add their exponents.
2. Quotient of Powers: When dividing two expressions with the same base, subtract the exponent of the denominator from the exponent of the numerator.
3. Power of a Power: When raising a power to another power, multiply the exponents.
4. Power of a Product: When raising a product to an exponent, distribute the exponent to each factor in the product.
5. Power of a Quotient: When raising a quotient to an exponent, apply the exponent to both the numerator and the denominator.
6. Zero Exponent: Any non-zero base raised to the exponent zero is equal to one.
7. Negative Exponent: A base with a negative exponent can be expressed as the reciprocal of the base raised to the positive exponent.
These laws allow you to simplify and manipulate expressions involving exponents effectively.
NCERT Solutions of Class 8th Chapter 12 Exponents and Powers Exercise 12.1 and 12.2
We try to teach you all Questions in easy way. We solve all chapter wise sums of maths textbook. In every chapter include NCERT solutions. For solutions of Exercise 12.1 and 12.2 click on Tabs :
Question 1.
Evaluate:
(i) 3-2
(ii) (-4)-2
(iii) (1/2)-5
Solution:
Question 2.
Simplify and express the result in power notation with a positive exponent.
Solution:
Question 3.
Find the value of
Solution:
Question 4.
Solution:
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
Question 6.
Evaluate:
Solution:
Question 7.
Simplify:
Solution:
