RD SHARMA Solutions for Class 9 Maths Chapter 2 - Exponents of Real Numbers

Simplify:

3(a⁴b³)¹⁰ × 5(a²b²)³

Simplify:

(2x^-2y³)³

Simplify:

Simplify:

Simplify:

Simplify:

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

a^a + b^b

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

a^b + b^a

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

(a + b)^ab

Prove that:

Prove that:

Prove that:

Prove that:

Prove that:

Prove that:

Simplify:

Simplify:

Simplify:

Simplify:

Solve the equation for x:

7^{2x + 3} = 1

Solve the equation for x:

2^x+1 = 4^x-3

Solve the equation for x:

2^{5x + 3} = 8^{x + 3}

Solve the equation for x:

Solve the equation for x:

Solve the equation for x:

2^{3x - 7} = 256

Solve the equation for x:

2^2x - 2^x+3 + 2⁴ = 0

Solve the equation for x:

3^{2x + 4} + 1 = 2.3^{x + 2}

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

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

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

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.

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

Simplify:

Prove that:

Show that:

Show that:

Show that:

Show that:

Note: Question modified

Show that:

(x^a-b)^a+b(x^b-c)^b+c(x^c-a)^c+a = 1

Show that:

Show that:

Show that:

Find the value of x if:

Find the value of x if:

5^{2x + 3} = 1

Find the value of x if:

Find the value of x if:

If x = 2^1/3 + 2^2/3, show that x³ - 6x = 6.

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

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

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

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

Solve the equation:

3^{x + 1} = 27 × 3⁴

Solve the equation:

Solve the equation

3^x-1 × 5^2y-3 = 225

Solve the equation:

Solve the equation:

Solve the equation:

If a and b are different positive primes such that

If a and b are different positive primes such that

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

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

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.

Simplify :

Simplify:

Show that:

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

If x = a^m+n, y = a^n+l and z = a^l+m, prove that x^myⁿz^l = zⁿy^lz^m.

The value of {2 - 3(2 - 3)³}³ is

(a) 5

(b) 125

(c) 1/5

(d) -125

The value of x - y^x-y when x = 2 and y = -2 is

(a) 18

(b) -18

(c) 14

(d) -14

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

If 8^x+1 = 64, what is the value of 3^2x+1?

(a) 1

(b) 3

(c) 9

(d) 27

If (2³)² = 4^x, then 3^x =

(a) 3

(b) 6

(c) 9

(d) 27

If x-² = 64, then x^1/3 + x⁰ =

(a) 2

(b) 3

(c) 3/2

(d) 2/3

If 9^x+2 = 240 + 9^x, then x =

(a) 0.5

(b) 0.2

(c) 0.4

(d) 0.1

If x is a positive real number and x² = 2, then x³ =

If (16)^2x+3 = (64)^x+3, then 4^2x-2 =

(a) 64

(b) 256

(c) 32

(d) 512