RD SHARMA SOLUTION CHAPTER – 2 Exponents of Real Numbers | CLASS 9TH MATHEMATICS-EDUGROWN

Chapter 2 Exponents of Real Numbers Exercise Ex. 2.1

Question 1(i)

Simplify:

3(a⁴b³)¹⁰ × 5(a²b²)³Solution 1(i)

Question 1(ii)

Simplify:

(2x^-2y³)³Solution 1(ii)

Question 1(iii)

Simplify:

Solution 1(iii)

Question 1(iv)

Simplify:

Solution 1(iv)

Question 1(v)

Simplify:

Solution 1(v)

Question 1(vi)

Simplify:

Solution 1(vi)

Question 2(i)

If a = 3 and b = -2, find the value of:

a^a + b^bSolution 2(i)

Question 2(ii)

If a = 3 and b = -2, find the value of:

a^b + b^aSolution 2(ii)

Question 2(iii)

If a = 3 and b = -2, find the value of:

(a + b)^abSolution 2(iii)

Question 3(i)

Prove that:

Solution 3(i)

Question 3(ii)

Prove that:

Solution 3(ii)

Question 4(i)

Prove that:

Solution 4(i)

Question 4(ii)

Prove that:

Solution 4(ii)

Question 5(i)

Prove that:

Solution 5(i)

Question 5(ii)

Prove that:

Solution 5(ii)

Question 6

Solution 6

Question 7(i)

Simplify:

Solution 7(i)

Question 7(ii)

Simplify:

Solution 7(ii)

Question 7(iii)

Simplify:

Solution 7(iii)

Question 7(iv)

Simplify:

Solution 7(iv)

Question 8(i)

Solve the equation for x:

7^{2x + 3} = 1Solution 8(i)

Question 8(ii)

Solve the equation for x:

2^x+1 = 4^x-3Solution 8(ii)

Question 8(iii)

Solve the equation for x:

2^{5x + 3} = 8^{x + 3}Solution 8(iii)

Question 8(iv)

Solve the equation for x:

Solution 8(iv)

Question 8(v)

Solve the equation for x:

Solution 8(v)

Question 8(vi)

Solve the equation for x:

2^{3x – 7} = 256Solution 8(vi)

Question 9(i)

Solve the equation for x:

2^2x – 2^x+3 + 2⁴ = 0Solution 9(i)

Question 9(ii)

Solve the equation for x:

3^{2x + 4} + 1 = 2.3^{x + 2}Solution 9(ii)

Question 10

If 49392 = a⁴b²c³, find the values of a, b and c, where a, b and c are different positive primes.Solution 10

Question 11

If 1176 = 2^a × 3^b × 7^c, find a, b and c.Solution 11

Question 12

Given 4725 = 3^a 5^b 7^c , find

1. the integral values of a, b and c
2. the values of 2^-a3^b7^c

Solution 12

Question 13

If a = xy^{p – 1}, b = xy^q-1 and c = xy^r-1, prove that a^q-rb^r-p c^p-q = 1.Solution 13

Chapter 2 Exponents of Real Numbers Exercise Ex. 2.2

Question 1(i)

Solution 1(i)

Question 1(ii)

Solution 1(ii)

Question 1(iii)

Solution 1(iii)

Question 1(iv)

Solution 1(iv)

Question 1(v)

Solution 1(v)

Question 1(vi)

Solution 1(vi)

Question 1(vii)

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

Solution 1(vii)

Question 2(i)

Solution 2(i)

Question 2(ii)

Simplify:

Solution 2(ii)

Question 2(iii)

Solution 2(iii)

Question 2(iv)

Solution 2(iv)

Question 2(v)

Solution 2(v)

Question 2(vi)

Solution 2(vi)

Question 2(vii)

Solution 2(vii)

Question 3(i)

Solution 3(i)

Question 3(ii)

Solution 3(ii)

Question 3(iii)

Solution 3(iii)

Question 3(iv)

Solution 3(iv)

Question 3(v)

Solution 3(v)

Question 3(vi)

Solution 3(vi)

Question 3(vii)

Prove that:

Solution 3(vii)

Question 3(viii)

Solution 3(viii)

Question 3(ix)

Solution 3(ix)

Question 4(i)

Show that:

Solution 4(i)

Question 4(ii)

Show that:

Solution 4(ii)

Question 4(iii)

Show that:

Solution 4(iii)

Question 4(iv)

Show that:

Note: Question modifiedSolution 4(iv)

Note: Question modifiedQuestion 4(v)

Show that:

(x^a-b)^a+b(x^b-c)^b+c(x^c-a)^c+a = 1Solution 4(v)

Question 4(vi)

Show that:

Solution 4(vi)

Question 4(vii)

Show that:

Solution 4(vii)

Question 4(viii)

Show that:

Solution 4(viii)

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10(i)

Solution 10(i)

Question 10(ii)

Solution 10(ii)

Question 10(iii)

Solution 10(iii)

Question 10(iv)

Solution 10(iv)

Question 10(v)

Solution 10(v)

Question 10(vi)

Find the value of x if:

Solution 10(vi)

Question 10(vii)

Find the value of x if:

5^{2x + 3} = 1Solution 10(vii)

Question 10(viii)

Find the value of x if:

Solution 10(viii)

Question 10(ix)

Find the value of x if:

Solution 10(ix)

Question 11

If x = 2^1/3 + 2^2/3, show that x³ – 6x = 6.Solution 11

Question 12

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

Question 13

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

Question 14

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

Question 15

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

Question 16(i)

Solve the equation:

3^{x + 1} = 27 × 3⁴Solution 16(i)

Question 16(ii)

Solve the equation:

Solution 16(ii)

Question 16(iii)

Solve the equation

3^x-1 × 5^2y-3 = 225Solution 16(iii)

Question 16(iv)

Solve the equation:

Solution 16(iv)

Question 16(v)

Solve the equation:

Solution 16(v)

Question 16(vi)

Solve the equation:

Solution 16(vi)

Question 17

Solution 17

Question 18(i)

If a and b are different positive primes such that

Solution 18(i)

Question 18(ii)

If a and b are different positive primes such that

(a + b)^-1(a^-1 + b^-1) = a^xb^y, find x + y + 2.Solution 18(ii)

Question 19

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

Question 20

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

Question 21(i)

Simplify :

Solution 21(i)

Question 21(ii)

Simplify:

Solution 21(ii)

Question 22

Show that:

Solution 22

Question 23(i)

If a = x^m+ny^l, b = x^n+ly^m and c = x^l+myⁿ, prove that a^m-nbn-lcl-m = 1.Solution 23(i)

Question 23(ii)

If x = a^m+n, y = a^n+l and z = a^l+m, prove that x^myⁿz^l = zⁿy^lz^m.Solution 23(ii)