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Chapter Analysis
Intermediate11 pages • EnglishQuick Summary
Chapter 10 in Class 8 Math, titled 'Exponents and Powers', introduces students to the concept of exponents, explaining how to express large numbers succinctly using powers of 10. It covers the laws of exponents, including multiplication, division, and taking powers of powers. The chapter also addresses negative exponents and illustrates their use in expressing small numbers. Practical applications such as expressing numbers in standard form are also discussed.
Key Topics
- •Introduction to exponents
- •Laws of exponents
- •Negative exponents
- •Standard form of numbers
- •Multiplicative inverse
- •Expressing numbers with positive and negative exponents
- •Operations with powers
Learning Objectives
- ✓Understand and use laws of exponents
- ✓Express large and small numbers using powers
- ✓Convert numbers to and from standard form
- ✓Work with negative exponents
- ✓Solve problems using the properties of exponents
Questions in Chapter
Evaluate: (i) 3–2 (ii) (– 4)–2 (iii) (1/2)^−5
Page 6
Simplify and express the result in power notation with positive exponent: (i) (–4)^5 ÷ (–4)^8
Page 6
Find the value of: (i) (3° + 4^−1) × 2^2
Page 6
Express the following numbers in standard form: (i) 0.0000000000085
Page 7
Express the following numbers in usual form: (i) 3.02 × 10^−6
Page 7
Additional Practice Questions
What is the value of (5^−1 × 3^−2) ÷ (6^−2)?
mediumAnswer: The value is 5/27, which simplifies as (5 × 1/9) ÷ (1/36) = 5/27.
Convert 4560000000 to standard form.
easyAnswer: In standard form, 4560000000 is written as 4.56 × 10^9.
If a^m × a^n = a^15 and a^n = a^5, what is the value of m?
mediumAnswer: Given a^m × a^n = a^15 and a^n = a^5, then a^(m+5) = a^15, so m = 10.
Simplify (−3)^3 × (−3)^−6.
mediumAnswer: The simplified form is (−3)^−3 = 1/((−3)^3) = 1/−27 = −1/27.
Find the multiplicative inverse of 10^−4.
easyAnswer: The multiplicative inverse of 10^−4 is 10^4.