Class 7 Exam > Class 7 Notes > RD Sharma Solutions for Class 7 Mathematics > RD Sharma Solutions - Ex-6.1, Exponents, Class 7, Math
Ex-6.1, Exponents, Class 7, Math RD Sharma Solutions | RD Sharma Solutions for Class 7 Mathematics PDF Download
Q1. Find the values of each of the following :
(i) 132
(ii) 73
(iii) 34
Sol:
(i) 132 = 13×13
= 169
(ii) 73 = 7×7×7
= 4
(iii) 34 = 3×3×3×3
= 81
Q2. Find the value of each of the following :
(i) (−7)2
(ii) (−3)4
(iii) (−5)5
Sol:
We know that if ‘a’ is a natural number, then
(−a) even number = positive number
(−a) odd number = negative number
We have,
(i) (−7)2 = (-7) ×(-7)
= 49
(ii) (−3)4 = (-3) ×(-3) ×(-3) ×(-3)
= 81
(iii) (−5)5 = (-5) ×(-5) ×(-5) ×(-5) ×(-5)
= -3125
Q3. Simply :
(i) 3×102
(ii) 22×53
(iii) 33×52
Sol:
(i) 3×102 = 3×10×10
= 3×100
= 300
(ii) 22×53 = 2×2×5×5×5
= 4×125
= 500
(iii) 33×52 = 3×3×3×5×5
= 27×25
= 675
Q4. Simply :
(i) 32×104
(ii) 24×32
(iii) 52×34
Sol:
(i) 32×104 = 3×3×10×10×10×10
= 9×10000
= 90000
(ii) 24×32 = 2×2×2×2×3×3
= 16×9
= 144
(iii) 52×34 = 5×5×3×3×3×3
= 25×81
= 2025
Q5. Simply :
(i) (−2)×(−3)3
(ii) (−3)2×(−5)3
(iii) (−2)5×(−10)2
Sol:
(i) (−2)×(−3)3 = (-2) ×(-3) ×(-3) ×(-3)
= (-2) ×(-27)
= 54
(ii) (−3)2×(−5)3 = (-3) ×(-3) ×(-5) ×(-5) ×(-5)
= 9×(-125)
= -1125
(iii) (−2)5×(−10)2 = (-2) ×(-2) ×(-2) ×(-2) ×(-2) ×(-10) ×(-10)
= (-32) × 100
= -3200
Q6. Simply :
Sol:
Q7. Identify the greater number in each of the following
(i) 25 or 52
(ii) 34 or 43
(iii) 35 or 53
Sol:
(i) 25 or 52
= 25 = 2×2×2×2×2
= 32
= 52 = 5×5
= 25
Therefore, 25 52
(ii) 34 or 43
= 34 = 3×3×3×3
= 81
= 43 = 4×4×4
= 64
Therefore, 34 43
(iii) 35 or 53
= 35 = 3×3×3×3×3
= 243
= 53 = 5×5×5
= 125
Therefore, 35 53
(iii) 35 or 53
= 35 = 3×3×3×3×3
= 243
= 53 = 5×5×5
= 125
Therefore, 35 53
Q8. Express each of the following in exponential form
(i) (-5) ×(-5) ×(-5)
Sol:
Q9. Express each of the following in exponential form
(i) x ×x ×x ×x ×a ×a ×b ×b ×b
(ii) (-2) ×(-2) ×(-2) ×(-2) ×a×a×a
Sol:
(i) x ×x ×x ×x ×a ×a ×b ×b ×b = x4a2b3
(ii) (-2) ×(-2) ×(-2) ×(-2) ×a×a×a = (−2)4a3
Q10. Express each of the following numbers in exponential form
(i) 512
(ii) 625
(iii) 729
Sol:
(i) 512 = 29
(iii) 625 = 54
(iii) 729 = 36
Q11. Express each of the following numbers as a product of powers of their prime factors
(i) 36
(ii) 675
(iii) 392
Sol:
(i) 36 = 2×2×3×3
= 22×32
(ii) 675 = 3×3×3×5×5
= 33×52
(iii) 392 = 2×2×2×7×7
= 23×72
Q12. Express each of the following numbers as a product of powers of their prime factors
(i) 450
(ii) 2800
(iii) 24000
Sol:
(i) 450 = 2×3×3×5×5
= 2×32×52
(ii) 2800 = 2×2×2×2×5×5×7
= 24×52×7
(iii) 24000 = 2×2×2×2×2×2×3×5×5×5
= 25×3×53
Q13. Express each of the following as a rational number of the form p/q
Sol:
Q14. Express each of the following rational numbers in power notation
Sol:
Because 72 = 49 and 82 = 64
Because 43 = 64 and 53 = 125
Because 13 = 1 and 63 = 216
Q15. Find the value of the following
Sol:
= 9/8
Q16. If a= 2 and b = 3, the find the values of each of the followimg
(i) (a+b)a
(ii) (ab)b
(iii) (b/a)b
Sol:
(i) (a+b)a = (2+3)2
= (5)2
= 25
(ii) (ab)b = (2×3)3
= (6)3
= 216
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FAQs on Ex-6.1, Exponents, Class 7, Math RD Sharma Solutions - RD Sharma Solutions for Class 7 Mathematics
| 1. What are exponents? |  |
Ans. Exponents are mathematical notations that represent the repeated multiplication of a number by itself. They are also known as powers or indices. In an exponent expression, the base number is raised to a certain power or exponent. For example, in the expression 2^3, 2 is the base and 3 is the exponent. It means 2 multiplied by itself three times, which equals 8.
| 2. How do exponents work? | |
Ans. Exponents work by indicating the number of times a base number should be multiplied by itself. The exponent represents the power to which the base number is raised. For example, 2^3 means 2 raised to the power of 3. It can be calculated as 2 multiplied by itself three times: 2 x 2 x 2 = 8. Similarly, 5^2 means 5 raised to the power of 2, which is 5 x 5 = 25.
| 3. What are the laws of exponents? | |
Ans. The laws of exponents are rules that govern the manipulation and simplification of exponential expressions. Some common laws of exponents include:
- Product of Powers Law: When multiplying two exponential expressions with the same base, you add their exponents. For example, a^m * a^n = a^(m+n).
- Quotient of Powers Law: When dividing two exponential expressions with the same base, you subtract their exponents. For example, a^m / a^n = a^(m-n).
- Power of a Power Law: When raising an exponential expression to another exponent, you multiply the exponents. For example, (a^m)^n = a^(m*n).
- Negative Exponent Law: An expression with a negative exponent can be rewritten as the reciprocal of the same expression with a positive exponent. For example, a^(-m) = 1/a^m.
These laws help simplify and manipulate exponential expressions efficiently.
| 4. How do exponents relate to multiplication and division? | |
Ans. Exponents are closely related to multiplication and division. When multiplying two exponential expressions with the same base, you add their exponents. For example, a^m * a^n = a^(m+n). This means you can simplify the multiplication of exponential expressions by adding their exponents.
Similarly, when dividing two exponential expressions with the same base, you subtract their exponents. For example, a^m / a^n = a^(m-n). This allows you to simplify the division of exponential expressions by subtracting their exponents.
These relationships between exponents, multiplication, and division make it easier to perform calculations and simplify expressions involving exponents.
| 5. How are exponents used in real-life applications? | |
Ans. Exponents are used in various real-life applications. Some examples include:
1. Compound Interest: The formula for calculating compound interest involves the use of exponents. The interest earned on an investment is usually compounded annually or at regular intervals, and the exponent represents the number of compounding periods.
2. Population Growth: Exponential growth models are commonly used to predict population growth over time. The exponent represents the growth rate, and it helps analyze how populations increase exponentially.
3. Computing: Exponents are used in computer programming and scientific calculations to represent large numbers or perform complex calculations efficiently.
4. Physics: Exponents are used in physics equations to represent physical quantities like force, energy, and velocity. They help express these quantities in a concise and mathematical manner.
Overall, exponents play a significant role in various fields, helping with calculations, predictions, and representing quantities in a compact form.
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