RD Sharma Class 9 Solutions Chapter 2 Exponents of Real Numbers

RD Sharma Class 9 Chapter 2 Exponents of Real Numbers Ex 2.1

Question 1.
Simplify the following:

Solution:

Question 2.
If a = 3 and b =-2, find the values of:
(i) a^a+ b^b
(ii) a^b + b^a(iii) (a+b)^abSolution:

Question 3.
Prove that:

Solution:

Question 4.
Prove that

Solution:

Question 5.
Prove that

Solution:

Question 6.

Solution:

Question 7.
Simplify the following:

Solution:

Question 8.
Solve the following equations for x:

Solution:

Question 9.
Solve the following equations for x:

Solution:

Question 10.
If 49392 = a⁴b²V³, find the values.of a, b and c, where a, b and c are different positive primes.
Solution:

Question 11.
If 1176 = 2^a x 3^b x T^c, find a, 6 and c.
Solution:

Question 12.
Given 4725 = 3^a5^b7^c, find:
(i) the integral values of a, b and c
(ii) the value of 2^-a 3^b 7^c
Solution:

Question 13.
If a = xy^p-1, b = xy ^q^-1 and c = xy^r-1, prove that a^q-rb^r-pc^p-q = 1
Solution:

RD Sharma Class 9 Solutions Chapter 2 Exponents of Real Numbers E x 2.2

Question 1.
Assuming that x, y, z are positive real numbers, simplify each of the following:

Solution:

Question 2.
Simplify:

Solution:

Question 3.
Prove that:

Solution:

Question 4.
Show that:

Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.
Find the values of x in each of the following:

Solution:

Question 11.
If x = 2¹^/3 + 2^2/3, show that x³ – 6x = 6.
Solution:

Question 12.
Determine (8x)^x, if 9^x^{+ 2} = 240 + 9^x.
Solution:

Question 13.
If 3^x⁺¹ = 9^x-², find the value of 2^{1 +x}.
Solution:

Question 14.
If 3^4x = (81)^-1 and 10^1/y = 0.0001, find the value of 2^-x+4ySolution:

Question 15.
If 5^3x = 125 and 10^y = 0.001 find x and y.
Solution:

Question 16.
Solve the following equations:

Solution:

Question 17.

Solution:

Question 18.
If a and b are different positive primes such that

Solution:

Question 19.
If 2^x x 3^y x 5^z = 2160, find x, y and z. Hence, compute the value of 3^x x 2^-y x 5^-z.
Solution:

Question 20.
If 1176 = 2^a x 3^b x 7^c, find the values of a, b and c. Hence, compute the value of 2^a x 3^b x 7^-c as a fraction.
Solution:

Question 21.
Simplify:

Solution:

Question 22.
Show that:

Solution:

Question 23.

Solution:

RD Sharma Class 9 Chapter 2 Exponents of Real Numbers VSAQS

Question 1.
Write (625)^–^1/4 in decimal form.
Solution:

Question 2.
State the product law of exponents:
Solution:
x^m x xⁿ = x^{m +n}

Question 3.
State the quotient law of exponents.
Solution:
x^m ÷ xⁿ = x^{m -n}

Question 4.
State the power law of exponents.
Solution:
(x^m)ⁿ =x^{m x n} = x^mn

Question 5.
If 2⁴ x 4² – 16^x, then find the value of x.
Solution:

Question 6.

Solution:

Question 7.
Write the value of \(\sqrt [ 3 ]{ 7 }\) x \(\sqrt [ 3 ]{ 49 }\) .
Solution:

Question 8.

Solution:

Question 9.
Write the value of \(\sqrt [ 3 ]{ 125×27 }\)
Solution:

Question 10.

Solution:

Question 11.

Solution:

Question 12.

Solution:

Question 13.

Solution:

Question 14.
If (x – 1)³ = 8, what is the value of (x + 1)²?
Solution:

Class 9 RD Sharma Solutions Chapter 2 Exponents of Real Numbers MCQS

Mark the correct alternative in each of the following:
Question 1.
The value of {2 – 3 (2 – 3)³}³ is
(a) 5
(b) 125
(c) \(\frac { 1 }{ 5 }\)
(d) -125
Solution:
{2 – 3 (2 – 3)³}³ = {2 – 3 (-1)³}³= {2 – 3 x (-1)}³= (2 + 3)³ = (5)³= 125 (b)

Question 2.
The value of x – y^x-y when x = 2 and y = -2 is
(a) 18
(b) -18
(c) 14
(d) -14
Solution:
x = 2, y = -2
x-y^x-y = 2 – (-2)^{2 – (-2)}= 2 – (-2)²⁺² = 2 – (-2)⁴= 2 – (+16) = 2 – 16 = -14 (d)

Question 3.
The product of the square root of x with the cube root of x, is
(a) cube root of the square root of x
(b) sixth root of the fifth power of x
(c) fifth root of the sixth power of x
(d) sixth root of x
Solution:

Question 4.
The seventh root of x divided by the eighth root of x is

Solution:

Question 5.
The square root of 64 divided by the cube root of 64 is
(a) 64
(b) 2
(c) \(\frac { 1 }{ 2 }\)
(d) 64^{\(\frac { 2 }{ 3 }\)}Solution:

Question 6.
Which of the following is (are) not equal to

Solution:

Question 7.
When simplified (x^–¹ + y^–¹)^–¹ is equal to

Solution:

Question 8.
If 8^x⁺¹ = 64, what is the value of 3 ^2x⁺¹?
(a) 1
(b) 3
(c) 9
(d) 27
Solution:

Question 9.
If (2³)² = 4^x then 3^x =
(a) 3
(b) 6
(c) 9
(d) 27
Solution:

Question 10.
If x^-2= 64, then x^{\(\frac { 1 }{ 3 }\)} + x°=
(a) 2
(b) 3
(c) \(\frac { 3 }{ 2 }\)
(c) \(\frac { 2 }{ 3 }\)
Solution:

Question 11.
When simplified ( –\(\frac { 1 }{ 27 }\))^{\(\frac { -2 }{ 3 }\)}
(a) 9
(b) -9
(c) \(\frac { 1 }{ 9 }\)
(d) –\(\frac { 1 }{ 9 }\)
Solution:

Question 12.
Which one of the following is not equal to

Solution:

Question 13.
Which one of the following is not equal to

Solution:

Question 14.
If a, b, c are positive real numbers, then

Solution:

Question 15.

Solution:

Question 16.

Solution:

Question 17.

Solution:

Question 18.

Solution:

Question 19.

Solution:

Question 20.

Solution:

Question 21.
The value of {(23 + 2²)^2/3+ (150 -29)^1/2}² is
(a) 196
(b) 289
(c) 324
(d) 400
Solution:
{(23 + 2²)^2/³ + (150 – 29)^1/2}²= [(23×4)^{\(\frac { 2 }{ 3 }\)} +(150 – 29)^{\(\frac { 1 }{ 2 }\)} ]²= [(27)^{\(\frac { 2 }{ 3 }\)} + (121)^{\(\frac { 1 }{ 2 }\)} ]²= [(3³)³ +(11²)^{\(\frac { 1 }{ 2 }\)}]² = (9 + 11)²= (20)² = 400 (d)