Class 8 Exam > Class 8 Notes > RD Sharma Solutions for Class 8 Mathematics > RD Sharma Solutions - Chapter 2 - Powers (Ex-2.2) Part- 2 Class 8 Math
Chapter 2 - Powers (Ex-2.2) Part- 2 Class 8 Math RD Sharma Solutions | RD Sharma Solutions for Class 8 Mathematics PDF Download
Question 8: By what number should (−5) −1 be multiplied so that the product is (−8) −1
Answer 8:
Let the number be x.
According to the question, 
Question 9: By what number should (15) −1 be multiplied so that the product may be equal to (−5) −1 ?
Answer 9:
Let the required number be x.
Therefore,
x=−3
Hence, the required number is −3.
Question 10:
By what number should (−15)−1 be divided so that the quotient may be equal to (−5)−1?
Answer 10:
Expressing in fractional form, we get:
(−15)−1 = −1/15, ---> (a−1 = 1/a)
and
(−5)−1 = −1/5 ---> (a−1 = 1/a)
We have to find a number x such that
Solving this equation, we get:
Hence, (−15)−1 should be divided by 1/3 to obtain (−5)−1.
Question 11:
By what number should (5/3)−2 be multiplied so that the product may be (73)−1?
Answer 11:
Expressing as a positive exponent, we have:
---> (a−1 = 1/a) 
---> ((a/b)n = (an)/(bn)) 
and(7/3)−1 = 3/7. ---> (a−1 = 1/a)
We have to find a number x such that
Multiplying both sides by 25/9, we get:
Hence, (5/3)−2 should be multiplied by 25/21 to obtain (7/3)−1.
Question 12:
Find x, if
Answer 12:
(i) We have:
(am×an = am+n)
x = 3
(ii) We have:
(am×an = am+n)
x = 6
(iii) We have:
x = 1/2
(iv) We have:
x = 10/3
(v) We have:
(vi) We have:
Question 13:
Answer 13:
(i) First, we have to find x.
x = 322×23-4 = Hence, x−2 is:
(ii) First, we have to find x.
Hence, the value of x−1 is:
(i) First, we have to find x.
x = 322×23-4 = Hence, x−2 is:
(ii) First, we have to find x.
Hence, the value of x−1 is:
Question 14: Find the value of x for which 52x ÷ 5−3 = 55.
Answer 14:
We have:
hence, x is 1.
The document Chapter 2 - Powers (Ex-2.2) Part- 2 Class 8 Math RD Sharma Solutions | RD Sharma Solutions for Class 8 Mathematics is a part of the Class 8 Course RD Sharma Solutions for Class 8 Mathematics.
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FAQs on Chapter 2 - Powers (Ex-2.2) Part- 2 Class 8 Math RD Sharma Solutions - RD Sharma Solutions for Class 8 Mathematics
| 1. How do you find the value of a number raised to a power? |  |
Ans. To find the value of a number raised to a power, you need to multiply the number by itself as many times as the power indicates. For example, if you have to find the value of 2 raised to the power of 3 (2^3), you would multiply 2 by itself three times: 2 x 2 x 2 = 8. Therefore, 2^3 = 8.
| 2. What is the meaning of a negative exponent? | |
Ans. A negative exponent indicates the reciprocal of a number raised to a positive exponent. For example, if you have 2 raised to the power of -3 (2^-3), it means the reciprocal of 2^3, which is 1/2^3 or 1/8. Therefore, 2^-3 = 1/8.
| 3. How do you simplify expressions with exponents? | |
Ans. To simplify expressions with exponents, you can use the rules of exponents. These rules include multiplying exponents with the same base, dividing exponents with the same base, and raising a power to another power. By applying these rules, you can simplify complex expressions and make them easier to evaluate.
| 4. What is the difference between the exponent and the base of a power? | |
Ans. In a power, the base is the number that is multiplied by itself, while the exponent represents the number of times the base is multiplied. For example, in 3^2, 3 is the base and 2 is the exponent. The base is the number being raised to a power, and the exponent tells us how many times the base is multiplied.
| 5. How are powers used in real-life applications? | |
Ans. Powers are used in various real-life applications such as scientific calculations, engineering, finance, and computer programming. They help in modeling exponential growth and decay, calculating compound interest, analyzing population growth, and understanding physical quantities like distance, energy, and volume. Powers provide a concise way to express repeated multiplication and are essential in many fields of study and applications.
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