Class 9 Exam > Class 9 Notes > RD Sharma Solutions for Class 9 Mathematics > RD Sharma Solutions Ex-2.2, (Part - 2), Exponents Of Real Numbers, Class 9, Maths
RD Sharma Solutions Ex-2.2, (Part - 2), Exponents Of Real Numbers, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics PDF Download
show that x3 − 6x = 6
x3 − 6x = 6
Putting cube on both the sides, we get
As we know, (a+b)3 = a3 + b3 + 3ab(a+b)
x3 = 6 + 6x
x3 – 6x = 6
Hence proved
12. Determine (8x)x, if 9x+2 = 240 + 9x.
9x+2 = 240 + 9x
9x .92 = 240 + 9x
Let 9x be y
81y = 240 + y
81y – y = 240
80y = 240
y = 3
Since, y = 3
Then,
9x = 3
32x = 3
Therefore, x = 1/2
= 2
Therefore (8x)x = 2
13. If 3x+1 = 9x-2, find the value of 21+x
3x+1 = 9x-2
3x+1 = 32x-4
x + 1 = 2x – 4
x = 5
Therefore the value of 21+x = 21+5 = 26 = 64
14. If 34x = (81)-1 and (10)1/y = 0.0001, find the value of 2-x+4y.
34x = (81)-1 and (10)1/y = 0.0001
34x = (3)-4
x = -1
And (10)1/y = 0.0001
(10)1/y = (10)−4
To find the value of 2-x+4y, we need to substitute the value of x and y
15. If 53x = 125 and 10y = 0.001. Find x and y.
53x = 125 and 10y = 0.001
53x = 53
x = 1
Now,
10y = 0.001
10y = 10-3
y = -3
Therefore, the value of x = 1 and the value of y = -3
16. Solve the following equations
(i) 3x+1 = 27×34
3x+1 = 33×34
3x+1 = 33+4
x + 1 = 3 + 4 [By equating exponents]
x + 1 = 7
x = 7 − 1
x = 6
24x = 23
4x = 3 (By equating exponents)
x = 3/4
(By equating exponents)
(iii). 3x−1×52y−3 = 225
3x−1×52y−3 = 32×52
x−1 = 2 [By equating exponents]
x = 3
3x−1×52y−3 = 32×52
2y−3 = 2 [By equating exponents]
2y = 5
y = 5/2
3x+3 = 4y+8 —eq1
3(3x+3) = 6+2x+24
9x+9 = 30+2x
7x = 21
x = 21/7
x = 3
Putting value of x in eq2
2x−2−3+2x = −3x [By equating exponents]
4x+3x = 5
7x = 5
x = 5/7
[By equating exponents]
17. If a and b are distinct positive primes such that 
find x and y
18.If a and b are different positive primes such that
axby find x and y
(ii) (a+b)−1(a−1+b−1) = axby,find x and y
=(ab)−1 = a−1b−1
By equating exponents
x = −1,y = −1
Therefore x+y+2 = −1−1+2 = 0
19. If 2x×3y×5z = 2160 , find x,y and z. Hence compute the value of 3x×2−y×5−z
20. If 1176 = 2a×3b×7c, find the values of a,b and c. Hence compute the value of 2a×3b×7−c as a fraction
We have to find the value of 
= 24/49
21. Simplify
22. Show that
Hence LHS = RHS
23.
(i) 
= x0 y0
= 1
The document RD Sharma Solutions Ex-2.2, (Part - 2), Exponents Of Real Numbers, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics is a part of the Class 9 Course RD Sharma Solutions for Class 9 Mathematics.
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FAQs on RD Sharma Solutions Ex-2.2, (Part - 2), Exponents Of Real Numbers, Class 9, Maths - RD Sharma Solutions for Class 9 Mathematics
| 1. What are exponents and how are they used in real numbers? |  |
Ans. Exponents are a way to represent repeated multiplication of a number by itself. In real numbers, exponents are used to express very large or very small numbers in a concise and convenient form. For example, the number 10 raised to the power of 3 (10^3) represents 10 multiplied by itself three times (10 x 10 x 10), which is equal to 1000.
| 2. How do exponents affect the value of a real number? | |
Ans. Exponents can significantly impact the value of a real number. When the exponent is positive, it indicates repeated multiplication and results in a larger value. Conversely, when the exponent is negative, it indicates repeated division and leads to a smaller value. For instance, 2^3 equals 2 x 2 x 2, which is 8, while 2^-3 equals 1/(2 x 2 x 2), which is 1/8 or 0.125.
| 3. What is the significance of the exponent 0 in real numbers? | |
Ans. The exponent 0 in real numbers has a special significance. Any non-zero number raised to the power of 0 is always equal to 1. For example, 5^0 is equal to 1, as there are no repeated multiplications involved. This property is based on the idea that any number divided by itself is equal to 1.
| 4. How can exponents be used to simplify calculations with real numbers? | |
Ans. Exponents can simplify calculations with real numbers by reducing the number of operations required. Instead of performing repeated multiplications or divisions, we can use exponents to represent the same calculations more concisely. For instance, instead of calculating 2 x 2 x 2 x 2, we can simply write 2^4. This simplifies calculations and makes them easier to solve.
| 5. Can exponents be used with all types of real numbers? | |
Ans. Exponents can be used with all types of real numbers, including both integers and fractions. While exponents are commonly associated with positive whole numbers, they can also be negative, zero, or fractions. This flexibility allows us to represent a wide range of values and perform various mathematical operations using exponents.
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