## 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)^{ab
}Solution:

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 = a^{4}b^{2}V^{3}, 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^{a}5^{b}7^{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-r }b^{r-p }c^{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 = 2^{1}^{/3} + 2^{2/3}, show that x^{3} – 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+4y
}Solution:

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 x^{n} = x^{m +n}

Question 3.

State the quotient law of exponents.

Solution:

x^{m} ÷ x^{n} = x^{m -n}

Question 4.

State the power law of exponents.

Solution:

(x^{m})^{n} =x^{m x n} = x^{mn}

Question 5.

If 2^{4} x 4^{2} – 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 (2^{3})^{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 + 2^{2})^{2/3}+ (150 -29)^{1/2}}^{2} is

(a) 196

(b) 289

(c) 324

(d) 400

Solution:

{(23 + 2^{2})^{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
}= [(3^{3})^{3} +(11^{2})^{\(\frac { 1 }{ 2 }\)}]^{2} = (9 + 11)^{2
}= (20)^{2} = 400 (d)

Question 22.

(256)^{0.16}x (256)^{0.09
}(a) 4

(b) 16

(c) 64

(d) 256.25

Solution:

Question 23.

If 10^{2y} = 25, then 10^{-y} equals

Solution:

Question 24.

If 9^{X }^{+} ^{2} = 240 + 9^{X}. then x =

(a) 0.5

(b) 0.2

(c) 0.4

(d) 0.1

Solution:

Question 25.

If x is a positive real number and x^{2} = 2, then x^{3} =

(a) \(\sqrt { 2 } \)

(b) 2\(\sqrt { 2 } \)

(c) 3\(\sqrt { 2 } \)

(d) 4

Solution:

Question 26.

Solution:

Question 27.

Solution:

Question 28.

Solution:

Question 29.

Solution:

Question 30.

Solution:

Question 31.

Solution:

Question 32.

Solution:

Question 33.

If (16)^{2x + 3} = (64)^{x + 3} , then 4^{2x – 2} =

(a) 64

(b) 256

(c) 32

(d) 512

Solution:

Question 34.

Solution:

Question 35.

Solution:

Question 36.

Solution:

Question 37.

Solution:

Question 38.

Solution:

Question 39.

Solution:

Question 40.

Solution:

RD Sharma Class 9th Solutions Chapter 2 Exponents of Real Numbers Exercise 2.1